Laboratorio 2
Angel Cordoba
2025-09-17
Simulación de Variables Aleatorias no uniformes en R
En un centro de soporte técnico de una empresa de software, llegan solicitudes de usuarios que deben ser atendidas por ingenieros de sistemas. Se quiere modelar el proceso de llegada y atención de solicitudes con distribuciones de probabilidad, y simular el sistema con R.
1. Llegadas de solicitudes
Suponga que, en promedio, llegan 5 solicitudes por hora al sistema.
A. Genere 5000 valores aleatorios que representen el número de solicitudes que llegan en cada hora.
B. Interprete el resultado.
C. Realice un gráfico de barras de las frecuencias.
D. Determine la probabilidad impírica de lleguen menos de 3 solicitudes.
promSolicitudes <- 5
solicitudes <- rpois(5000, promSolicitudes)
solicitudes## [1] 3 5 4 1 4 11 6 11 2 3 3 6 5 4 7 8 4 4 5 2 3 6 9 2
## [25] 3 3 4 3 1 5 2 3 6 5 6 3 1 4 7 4 8 5 8 3 5 1 5 4
## [49] 2 4 3 5 4 5 3 8 4 4 4 7 13 8 6 5 4 8 2 1 3 4 5 7
## [73] 1 3 2 4 5 3 2 3 6 5 3 5 5 6 4 7 4 4 6 3 7 11 9 5
## [97] 2 9 6 3 2 4 5 5 7 5 2 9 6 4 7 6 3 5 5 7 9 6 4 2
## [121] 5 4 7 5 5 6 7 4 6 5 4 8 7 8 4 0 5 7 6 7 1 7 4 7
## [145] 7 9 8 5 7 3 4 2 6 6 4 8 3 7 7 5 5 5 7 4 6 2 1 11
## [169] 2 4 8 4 6 2 4 4 6 4 4 5 8 2 6 5 2 2 8 3 0 3 3 6
## [193] 5 2 3 9 6 3 1 3 2 2 7 5 2 8 3 2 6 3 4 7 3 8 3 3
## [217] 4 4 7 9 4 4 9 5 5 6 1 3 4 5 6 6 10 7 6 2 7 6 2 5
## [241] 6 1 5 3 5 8 3 5 4 5 4 3 7 5 4 3 3 8 2 3 6 5 10 7
## [265] 6 2 4 3 4 7 10 1 8 7 3 6 5 9 8 8 1 5 4 4 2 3 3 6
## [289] 7 7 5 9 7 7 3 5 5 2 6 4 4 6 4 2 6 2 6 5 7 6 1 4
## [313] 5 5 3 4 4 5 5 3 2 7 2 8 2 3 5 9 4 4 6 3 9 5 6 8
## [337] 1 1 4 7 1 9 5 6 8 6 4 2 3 5 2 3 6 5 3 2 6 8 1 7
## [361] 6 1 3 4 3 4 4 4 3 2 6 3 2 4 3 3 5 2 10 7 5 4 11 3
## [385] 5 8 6 8 4 7 1 6 4 6 5 4 5 5 5 6 11 11 5 8 7 5 5 2
## [409] 10 8 8 5 3 9 2 9 8 8 6 5 6 1 2 6 6 7 4 5 5 7 5 1
## [433] 12 7 8 3 7 5 5 6 1 3 2 4 5 5 2 4 3 4 7 2 5 7 5 5
## [457] 1 4 6 5 3 9 5 2 3 9 5 2 4 2 5 4 8 6 8 4 6 7 3 9
## [481] 4 5 5 0 5 4 10 7 3 8 3 3 4 5 6 7 4 3 7 7 2 3 6 7
## [505] 5 5 2 5 5 6 4 8 1 3 3 3 5 8 1 5 6 4 6 4 6 2 4 8
## [529] 3 2 6 6 1 6 9 6 5 5 11 5 9 3 4 4 4 5 9 5 3 4 4 3
## [553] 4 4 3 5 5 3 6 6 3 2 8 4 4 5 6 7 5 8 1 5 3 7 3 6
## [577] 3 2 6 4 4 3 6 5 5 1 10 6 6 2 6 6 3 5 4 6 10 8 5 9
## [601] 6 3 3 5 4 6 3 3 7 2 8 1 8 7 7 3 1 5 5 6 3 9 3 3
## [625] 0 9 9 7 5 7 4 8 7 5 10 5 6 7 4 8 6 1 5 9 6 10 6 7
## [649] 4 2 5 4 7 4 5 5 2 4 5 5 4 3 2 5 7 6 3 4 7 10 5 8
## [673] 4 3 5 3 2 5 2 1 6 4 5 6 10 5 5 5 7 4 3 3 4 5 2 1
## [697] 2 7 6 11 3 4 6 5 4 6 9 4 5 2 5 4 9 5 7 4 3 3 4 6
## [721] 5 7 7 8 5 3 3 3 2 4 4 7 4 4 2 3 5 11 5 5 5 7 8 6
## [745] 6 4 5 4 4 8 7 6 8 4 2 11 5 3 4 7 5 6 6 5 4 3 5 3
## [769] 6 5 3 5 9 11 3 9 6 3 4 7 5 5 5 2 7 4 9 4 1 4 2 6
## [793] 7 6 4 6 5 8 4 5 10 4 4 8 7 5 8 5 1 4 5 7 4 3 5 6
## [817] 2 5 1 6 0 2 6 8 7 3 3 10 5 6 7 3 3 9 4 2 7 6 5 7
## [841] 11 2 4 11 8 5 7 4 2 5 8 5 5 5 6 4 4 2 6 4 3 7 3 4
## [865] 6 3 6 7 5 4 3 3 8 4 6 9 8 3 5 5 6 5 3 6 8 4 7 4
## [889] 7 3 6 3 5 7 1 7 7 5 5 4 5 3 6 4 5 7 5 6 2 10 5 7
## [913] 4 2 2 9 3 2 5 2 2 6 2 6 8 7 3 9 1 6 7 9 6 7 5 1
## [937] 4 2 5 5 5 4 9 6 5 4 7 3 6 5 3 5 7 6 3 6 4 3 5 7
## [961] 11 6 4 5 8 8 4 7 6 5 5 7 3 2 2 6 5 7 6 6 10 6 8 8
## [985] 6 7 9 8 3 3 10 5 8 1 4 8 3 4 2 8 4 6 3 5 8 7 9 9
## [1009] 1 3 6 3 6 4 2 8 4 8 3 2 4 6 3 5 0 6 7 5 8 5 3 5
## [1033] 5 6 6 2 4 7 6 6 4 3 4 9 1 4 8 4 6 4 9 10 7 6 4 1
## [1057] 3 8 5 3 4 1 3 4 2 7 5 4 4 2 7 5 0 10 2 3 3 4 2 2
## [1081] 1 7 2 7 5 5 3 4 5 1 4 4 6 10 6 3 4 10 4 4 3 4 7 4
## [1105] 4 8 7 1 6 5 8 8 5 3 6 3 3 5 8 4 10 3 5 5 4 2 8 4
## [1129] 5 4 3 6 10 6 3 6 7 5 5 7 7 7 8 5 3 7 5 3 3 7 3 3
## [1153] 6 7 3 5 3 5 0 5 5 10 6 3 1 6 3 3 5 4 10 2 4 6 4 4
## [1177] 3 4 10 2 7 3 6 5 7 5 8 3 5 8 11 2 4 4 2 4 3 2 3 4
## [1201] 4 5 5 4 4 7 6 6 5 7 7 6 7 2 6 7 2 2 7 6 2 4 7 7
## [1225] 3 6 7 6 6 3 4 4 1 5 5 9 2 4 6 2 3 9 3 1 5 3 5 4
## [1249] 4 8 4 4 3 5 8 8 3 2 7 3 8 5 7 6 3 2 3 7 12 5 5 1
## [1273] 4 4 8 6 5 4 6 5 4 7 4 6 6 3 4 10 9 4 4 5 6 4 5 3
## [1297] 1 6 7 5 2 1 10 3 6 10 5 7 2 6 6 8 8 2 7 5 7 7 1 3
## [1321] 5 2 5 3 6 6 7 3 4 14 5 3 3 2 7 7 7 4 8 9 5 6 5 5
## [1345] 5 5 4 9 6 7 3 8 5 8 7 5 8 5 4 7 2 8 4 8 7 2 2 2
## [1369] 5 5 9 4 2 7 4 10 5 9 4 3 4 6 5 2 3 4 3 4 9 3 9 6
## [1393] 1 4 6 4 7 6 3 6 6 2 3 5 9 2 2 3 6 7 7 5 7 5 3 4
## [1417] 4 4 8 7 4 5 4 4 2 6 5 7 2 6 9 6 5 9 6 4 8 5 4 3
## [1441] 5 2 7 2 6 8 6 6 4 7 3 6 8 5 5 5 8 4 4 5 4 4 8 4
## [1465] 3 5 2 4 8 8 7 5 4 3 2 4 4 2 2 4 5 6 3 3 8 4 4 3
## [1489] 3 4 7 6 6 4 2 1 6 2 8 3 3 1 6 5 4 5 7 5 2 5 6 4
## [1513] 1 4 3 1 4 7 1 5 3 1 5 6 3 5 2 3 6 4 3 3 3 2 4 6
## [1537] 5 2 2 4 4 9 6 5 5 2 5 4 6 7 7 2 7 5 7 2 4 4 4 3
## [1561] 5 8 7 4 3 2 6 7 6 9 3 6 4 3 2 7 2 5 5 7 5 2 7 11
## [1585] 5 12 0 3 7 4 8 4 4 5 5 3 4 6 4 8 6 8 3 5 3 6 4 5
## [1609] 2 7 3 5 5 4 3 4 5 4 5 5 4 2 5 5 1 6 4 4 6 8 4 5
## [1633] 4 7 3 3 4 7 5 6 4 3 5 4 1 6 3 7 3 6 6 9 8 4 9 4
## [1657] 3 2 6 2 6 7 2 7 6 0 4 4 5 6 6 4 7 9 5 7 4 6 6 3
## [1681] 6 9 8 6 3 6 4 7 2 6 4 7 5 5 5 10 1 5 7 5 4 6 6 2
## [1705] 6 6 6 2 6 8 9 9 4 10 4 8 3 6 3 4 12 2 1 1 8 8 2 6
## [1729] 8 7 5 3 9 9 3 7 5 9 10 7 3 6 2 10 2 6 4 6 2 5 6 3
## [1753] 4 2 7 2 1 8 6 5 4 7 5 5 3 5 4 4 4 11 5 4 2 3 7 9
## [1777] 4 6 11 3 9 4 3 1 6 6 4 4 7 2 2 8 4 13 9 6 0 8 1 4
## [1801] 6 3 6 4 8 3 3 4 4 6 4 4 4 5 7 3 3 5 4 6 7 5 6 6
## [1825] 8 6 4 5 5 3 7 7 2 2 4 5 4 3 7 9 6 4 6 6 5 6 11 4
## [1849] 12 3 2 6 4 5 1 6 4 1 4 6 2 10 2 3 7 2 2 6 5 2 2 6
## [1873] 2 4 2 9 6 2 3 4 5 6 7 6 6 9 5 2 6 4 3 2 6 5 4 1
## [1897] 6 2 6 6 3 7 7 5 3 6 4 2 4 4 4 10 3 7 6 4 2 3 5 7
## [1921] 5 8 5 6 2 3 9 7 4 6 8 4 3 1 10 6 5 7 1 6 7 8 8 4
## [1945] 5 7 3 3 4 7 6 9 3 5 5 7 3 7 6 6 4 8 8 5 6 5 4 5
## [1969] 5 5 9 4 1 4 4 3 2 3 6 3 5 6 5 5 6 8 4 2 1 5 4 8
## [1993] 4 7 4 9 7 5 9 1 6 10 5 5 5 4 8 3 5 5 6 5 4 7 9 6
## [2017] 9 3 4 1 2 5 4 2 6 3 5 6 4 4 4 3 3 6 6 4 0 4 2 4
## [2041] 7 6 5 5 6 6 2 1 8 6 6 5 5 5 5 4 3 4 7 5 4 9 9 5
## [2065] 6 3 5 5 5 6 6 5 9 6 11 1 5 6 5 4 7 8 6 1 6 5 9 9
## [2089] 5 2 7 6 5 3 5 6 3 9 4 2 1 8 4 2 6 4 4 5 5 3 7 5
## [2113] 5 3 7 2 6 4 3 6 4 5 3 4 9 4 9 4 7 4 4 3 7 4 1 9
## [2137] 5 3 5 3 6 6 3 10 8 4 2 5 10 9 7 6 7 4 5 8 4 5 4 9
## [2161] 9 5 2 3 5 6 10 3 3 6 9 6 3 10 3 7 7 5 7 1 2 5 5 6
## [2185] 6 10 4 3 4 5 5 3 6 6 3 3 5 7 8 4 2 5 8 9 4 4 6 5
## [2209] 7 5 3 4 5 5 5 6 3 5 5 2 7 6 2 5 1 3 4 5 6 7 8 4
## [2233] 1 5 7 3 8 3 5 6 3 4 2 5 7 4 6 3 3 8 2 1 5 4 4 10
## [2257] 3 8 7 8 4 10 4 3 7 2 6 6 8 5 6 7 6 4 7 1 5 6 4 6
## [2281] 8 5 9 7 3 2 5 3 4 6 5 6 7 6 10 3 3 3 5 5 9 5 6 6
## [2305] 4 10 3 8 3 5 9 6 4 3 8 5 9 4 1 3 7 5 5 5 3 8 4 5
## [2329] 2 5 7 4 6 5 2 8 6 7 4 5 4 5 8 8 8 4 1 8 2 3 2 4
## [2353] 6 10 8 8 6 6 5 6 6 8 7 8 6 5 3 2 3 5 10 3 3 7 2 4
## [2377] 7 1 5 4 5 5 5 6 4 2 6 8 4 7 5 5 5 3 3 2 6 5 4 3
## [2401] 5 5 6 4 5 9 8 1 2 4 2 4 4 7 4 5 4 3 6 2 4 6 6 2
## [2425] 6 4 6 5 8 7 4 3 4 4 8 5 5 3 4 5 3 4 2 8 1 6 6 8
## [2449] 9 9 3 2 5 5 4 3 3 3 6 6 3 5 7 6 6 7 7 5 5 5 9 4
## [2473] 3 2 8 2 2 5 7 6 7 8 3 2 2 1 2 9 8 7 4 6 1 4 4 4
## [2497] 4 6 2 6 3 9 0 9 4 6 4 2 3 3 5 6 8 7 5 4 2 4 7 2
## [2521] 6 4 6 7 5 11 1 5 3 6 7 8 3 5 4 4 6 1 3 3 5 2 5 7
## [2545] 3 8 4 3 8 4 5 5 6 6 3 5 5 8 6 4 7 5 2 2 7 3 7 7
## [2569] 7 7 5 6 3 5 7 5 4 5 8 7 6 5 5 6 5 3 6 5 1 6 6 5
## [2593] 2 3 4 5 8 7 3 9 5 4 4 5 5 6 3 3 5 7 2 5 3 5 7 9
## [2617] 8 7 5 4 8 5 6 7 6 4 2 5 11 5 6 10 10 5 6 6 7 7 2 4
## [2641] 6 1 3 8 5 12 6 5 9 2 2 9 6 5 6 4 3 11 6 5 4 4 2 2
## [2665] 5 4 3 5 7 6 9 9 1 2 3 4 5 8 3 6 3 3 6 2 6 7 7 3
## [2689] 5 2 3 10 4 10 4 4 3 5 2 4 3 5 5 3 5 2 4 6 5 2 6 7
## [2713] 8 5 6 9 8 8 4 3 3 10 7 5 3 5 5 4 7 9 4 9 4 6 4 6
## [2737] 3 4 8 3 2 5 7 3 4 4 7 6 4 7 4 2 7 7 4 4 4 6 7 3
## [2761] 2 4 7 6 3 2 8 9 4 8 7 2 6 4 4 2 5 10 3 5 2 7 6 6
## [2785] 0 2 3 5 6 4 3 5 8 3 10 3 5 9 3 7 5 7 7 4 8 5 8 2
## [2809] 3 2 8 5 7 6 7 6 5 7 7 4 9 6 9 3 2 8 2 5 7 2 4 4
## [2833] 8 8 7 5 2 3 5 6 3 5 3 10 4 7 9 5 8 4 4 4 3 5 5 3
## [2857] 4 9 7 7 6 7 8 13 4 4 3 5 7 3 8 6 6 9 5 4 4 2 8 6
## [2881] 2 2 2 5 9 7 7 2 4 6 5 7 6 5 5 4 5 6 8 11 4 3 6 9
## [2905] 5 8 6 9 3 6 3 6 4 1 5 3 7 6 5 1 4 6 4 8 5 6 6 5
## [2929] 2 3 3 5 5 5 3 4 3 3 1 4 2 5 5 5 4 3 6 8 5 3 5 3
## [2953] 6 3 6 8 5 4 3 6 2 7 6 8 11 6 4 3 6 12 10 3 5 4 5 5
## [2977] 6 8 6 6 10 1 8 2 8 3 3 7 3 5 8 4 3 7 5 6 4 7 9 3
## [3001] 6 11 3 2 4 6 4 9 5 3 6 6 5 6 2 7 5 6 8 5 5 2 3 5
## [3025] 3 4 5 5 5 0 3 7 3 4 4 6 4 6 3 3 6 8 5 10 3 1 4 6
## [3049] 10 7 5 3 4 2 4 5 6 3 7 5 3 5 4 8 4 6 6 8 8 9 8 6
## [3073] 2 4 1 5 5 5 1 4 2 4 6 4 8 7 6 8 6 7 4 4 3 1 4 9
## [3097] 3 9 5 4 9 4 6 7 3 3 2 3 3 6 8 9 4 8 3 3 3 4 4 3
## [3121] 7 6 10 5 8 4 4 4 6 8 2 6 6 3 3 6 6 4 5 3 4 7 6 5
## [3145] 5 5 4 2 9 1 8 7 4 3 5 6 8 5 5 4 3 3 3 4 5 4 2 7
## [3169] 3 13 2 4 1 6 5 1 5 3 5 3 7 6 8 2 6 10 5 7 4 2 4 3
## [3193] 5 6 9 2 4 5 6 11 9 2 2 5 2 3 7 3 12 6 5 4 6 4 8 1
## [3217] 3 7 3 4 7 1 5 3 3 4 8 2 3 6 5 5 5 1 4 6 8 1 3 7
## [3241] 7 5 5 6 7 8 1 7 5 4 3 3 6 6 8 2 6 6 5 3 7 3 2 2
## [3265] 7 4 3 5 4 3 4 6 5 6 9 4 3 2 8 5 2 7 7 6 5 1 4 8
## [3289] 6 6 6 6 3 7 5 6 8 11 3 2 7 3 7 4 5 6 1 3 7 3 0 4
## [3313] 3 6 7 6 5 6 10 3 6 2 7 3 5 2 2 6 3 7 1 3 5 10 4 5
## [3337] 7 4 5 6 7 8 5 6 5 6 11 8 4 4 1 2 8 4 6 5 3 9 5 3
## [3361] 7 1 4 2 4 1 9 6 9 5 1 5 8 3 6 4 5 4 5 9 3 9 1 7
## [3385] 1 5 5 5 8 5 4 6 5 11 5 3 12 3 5 6 1 7 4 5 3 6 7 3
## [3409] 4 10 1 5 9 3 8 4 10 4 5 2 3 5 7 6 4 4 5 3 3 4 4 3
## [3433] 11 4 6 5 6 7 6 6 6 8 6 4 8 2 6 3 0 5 3 5 3 6 7 5
## [3457] 5 8 7 5 11 1 7 4 5 10 8 6 4 1 5 5 6 6 5 3 5 2 5 6
## [3481] 6 6 5 7 10 3 8 2 5 4 8 6 6 7 6 1 1 5 5 8 4 10 7 3
## [3505] 6 4 9 6 0 5 3 4 6 6 3 0 4 2 4 7 10 7 7 9 6 6 4 7
## [3529] 5 5 5 4 5 8 5 3 1 7 5 3 7 4 8 6 7 8 8 3 4 7 8 2
## [3553] 4 3 6 3 2 5 5 6 3 5 5 4 5 6 8 7 3 4 4 5 4 4 6 6
## [3577] 5 3 8 8 5 4 5 3 5 5 4 5 2 6 8 4 6 5 4 5 3 3 3 3
## [3601] 7 6 1 4 7 10 0 5 6 4 2 6 3 3 7 7 9 3 5 7 3 7 5 5
## [3625] 2 4 8 3 3 4 4 9 1 1 3 3 1 12 5 1 5 5 6 5 9 9 9 8
## [3649] 7 2 8 3 9 6 3 6 8 4 5 4 4 5 6 4 7 5 2 5 7 9 6 6
## [3673] 4 4 5 8 9 5 4 4 0 3 0 2 2 4 1 2 2 3 3 2 8 8 8 5
## [3697] 7 3 2 2 11 2 7 4 5 3 9 7 6 9 8 5 5 6 3 4 7 3 3 2
## [3721] 8 3 5 4 9 2 5 7 4 5 5 7 7 7 2 1 3 6 6 4 3 7 4 9
## [3745] 8 6 5 4 4 4 9 6 6 4 3 4 4 4 4 7 4 4 4 7 6 3 3 5
## [3769] 6 5 4 6 6 4 6 10 1 5 7 5 2 3 5 3 4 4 8 5 5 5 4 3
## [3793] 12 4 3 5 3 7 5 5 6 2 6 5 4 3 7 5 5 7 6 6 12 7 4 5
## [3817] 8 5 7 5 7 5 6 7 7 5 7 7 4 3 7 10 4 8 4 5 5 6 2 5
## [3841] 7 3 5 10 3 9 4 5 1 2 6 5 4 5 6 2 3 3 10 6 9 4 8 9
## [3865] 10 4 3 3 6 3 4 8 5 10 5 2 4 4 5 7 3 2 4 4 7 4 3 5
## [3889] 8 7 1 6 2 4 5 3 4 2 2 5 7 3 4 3 3 5 2 7 10 7 3 6
## [3913] 5 4 2 5 6 6 5 6 3 7 3 4 5 4 3 4 4 5 10 3 4 4 3 6
## [3937] 2 5 2 2 5 4 5 4 9 6 5 4 6 4 2 7 6 1 2 5 5 2 6 5
## [3961] 7 2 4 8 6 6 4 2 7 8 2 6 6 2 7 5 3 3 3 4 4 5 6 1
## [3985] 3 4 7 6 4 4 4 4 6 7 4 6 6 7 7 6 5 8 6 4 1 5 6 7
## [4009] 9 2 6 5 8 1 8 3 8 6 3 7 7 6 6 2 4 7 6 4 2 8 4 6
## [4033] 6 6 1 4 8 1 0 6 8 5 5 5 2 6 3 6 5 6 4 5 4 5 7 2
## [4057] 1 2 4 6 5 4 3 5 4 4 7 5 3 5 4 7 5 4 2 4 2 7 7 4
## [4081] 6 5 5 6 5 3 5 3 7 4 3 9 7 6 7 10 7 7 7 6 4 4 7 2
## [4105] 7 6 5 7 3 5 5 10 4 5 8 4 5 11 2 8 3 8 8 4 6 5 7 7
## [4129] 3 5 6 6 3 5 2 4 5 6 3 4 5 3 4 3 3 8 4 3 7 2 7 3
## [4153] 5 8 4 7 4 4 6 6 6 7 4 5 3 4 10 3 1 10 7 4 4 9 8 4
## [4177] 10 7 6 1 2 5 6 3 4 6 4 4 4 4 4 5 3 6 2 8 8 4 2 7
## [4201] 4 1 6 5 3 5 5 3 4 5 3 11 4 7 3 5 4 5 4 3 2 3 4 6
## [4225] 7 2 2 2 4 9 5 4 4 5 4 4 6 4 3 7 7 7 3 3 2 2 5 3
## [4249] 4 5 5 6 4 2 8 6 3 6 8 8 5 3 6 2 6 4 6 7 3 2 7 7
## [4273] 8 5 2 3 5 4 6 6 1 4 3 7 3 9 8 7 5 5 3 3 8 9 2 4
## [4297] 5 5 6 5 6 3 6 4 6 9 3 2 9 6 7 3 13 1 4 9 5 3 2 7
## [4321] 4 6 6 8 8 4 8 5 5 2 3 3 4 2 9 8 7 2 1 8 4 8 6 2
## [4345] 2 3 6 7 11 10 5 3 7 7 3 8 4 6 5 4 7 3 3 6 6 9 1 3
## [4369] 4 3 12 8 5 6 6 6 5 3 6 3 3 6 8 3 3 7 6 2 3 8 4 4
## [4393] 4 4 4 3 6 6 1 1 6 1 6 7 4 4 4 5 4 5 5 4 2 6 6 6
## [4417] 7 2 4 7 5 8 1 6 3 8 5 4 0 4 6 5 7 6 7 6 4 3 4 5
## [4441] 5 3 5 5 6 1 7 8 9 4 1 5 4 5 5 4 4 2 1 8 3 3 2 5
## [4465] 5 5 2 4 2 3 6 7 5 5 1 7 2 5 7 4 10 2 3 5 6 8 6 5
## [4489] 6 5 4 6 2 3 3 4 3 3 5 5 8 4 8 4 5 2 1 4 5 5 7 6
## [4513] 3 5 2 7 4 3 5 5 2 8 4 5 6 4 7 5 8 6 8 8 4 3 1 4
## [4537] 5 4 5 4 0 9 10 9 6 5 3 3 6 4 5 4 5 15 4 6 6 3 6 3
## [4561] 3 5 2 7 8 7 4 4 5 2 5 3 5 3 2 6 4 5 6 5 5 1 9 4
## [4585] 2 3 6 4 6 8 3 9 4 6 4 8 1 4 8 5 5 3 5 6 4 4 7 5
## [4609] 3 3 2 4 3 5 6 7 7 5 5 4 6 6 4 5 7 4 5 4 7 2 2 4
## [4633] 5 4 3 10 8 5 7 5 5 3 4 7 4 4 6 6 3 9 10 6 9 4 7 5
## [4657] 5 8 7 4 5 6 4 6 9 8 6 4 4 3 4 4 1 2 9 3 4 5 4 6
## [4681] 8 4 5 5 6 4 2 6 8 4 7 3 6 13 3 3 8 4 7 6 3 7 4 4
## [4705] 6 4 4 6 4 4 4 6 5 2 2 5 10 10 7 8 3 7 5 2 4 3 6 2
## [4729] 2 2 2 6 4 5 7 3 6 4 3 6 2 7 7 8 4 3 4 4 8 5 1 2
## [4753] 3 4 4 9 5 2 6 2 6 9 5 7 2 6 3 3 4 7 1 4 7 2 3 3
## [4777] 6 5 4 3 2 5 5 7 8 4 6 7 5 4 4 4 5 10 6 3 4 5 4 5
## [4801] 5 2 3 3 2 1 5 5 6 5 11 4 4 6 10 4 7 3 10 2 6 6 2 9
## [4825] 7 6 2 4 4 6 8 2 3 3 2 0 3 6 2 7 6 4 5 5 7 4 8 9
## [4849] 4 4 3 7 5 3 5 4 8 9 6 9 5 4 6 10 4 5 5 7 4 6 7 3
## [4873] 5 5 3 7 3 1 6 4 5 2 7 5 4 6 2 4 4 5 4 6 5 5 7 10
## [4897] 10 10 5 6 9 8 5 6 5 7 4 7 9 6 4 6 8 4 6 2 5 4 2 8
## [4921] 8 11 3 5 7 4 4 5 8 8 5 10 4 4 8 4 1 6 2 5 7 6 4 6
## [4945] 2 5 5 9 4 2 7 5 4 5 3 5 9 4 7 4 3 6 9 3 6 9 1 3
## [4969] 5 3 9 4 5 4 5 4 5 5 7 3 2 8 4 5 3 5 3 7 6 5 5 4
## [4993] 7 7 1 4 4 6 5 2hist(solicitudes, main = "Número de solicitudes que llegan en cada hora",col = "red")
probabilidad <- mean(solicitudes < 3)
probabilidad## [1] 0.126Interpretacion
Con esta simulación vimos que normalmente llegan unas 5 solicitudes por hora, aunque a veces pueden ser un poco menos o un poco más. El gráfico nos muestra que la mayoría de los casos se miran cerca de ese valor promedio. Además, se calculó que la probabilidad de que lleguen menos de 3 solicitudes en una hora es baja, alrededor del 12%.
2. Tiempos entre llegadas
El tiempo entre llegadas de solicitudes sigue una distribución Exponencial con media 12 minutos.
A. Genere 5000 tiempos entre llegadas.
B. Represente el histograma.
media <- 12
rate1<- 1/media
tiempoLlegada<- rexp(5000, rate1)
tiempoLlegada## [1] 1.745781e+01 2.909111e+00 4.760432e+00 2.094220e+01 4.863136e+01
## [6] 1.106356e+01 5.154455e+00 7.042660e+00 1.342748e+00 3.542831e+01
## [11] 8.576198e+00 1.024270e+01 9.669724e+00 1.693695e+01 1.647854e+00
## [16] 5.601145e+00 1.793441e+00 2.708323e+01 1.206964e+01 4.496388e+00
## [21] 5.964873e+00 8.908709e+00 1.669475e+01 5.243516e+00 6.637129e+00
## [26] 6.563662e+00 4.071072e-01 2.657696e+01 9.428116e+00 1.284120e+01
## [31] 4.651415e-01 1.753512e+01 8.482173e+00 6.505558e+00 3.703714e+01
## [36] 1.976173e+00 2.886026e+00 7.878790e+00 6.104279e+00 1.850565e+01
## [41] 4.371082e+00 1.002857e+01 3.481858e+01 1.300548e+01 4.346762e+00
## [46] 4.536029e+00 9.736743e-01 8.010953e-01 9.045673e-01 1.000038e+01
## [51] 6.351954e+00 8.210618e+00 9.294729e+00 2.302257e+01 5.984667e+00
## [56] 4.103075e+01 1.411638e+01 6.915657e+00 5.117430e+00 2.486588e+00
## [61] 1.742226e+00 7.063474e-02 1.541394e+01 3.203680e+00 2.268303e+01
## [66] 1.268444e+01 1.081514e+01 3.724046e+01 1.436970e+01 9.914554e-01
## [71] 2.198882e+00 2.489989e+01 2.371044e+01 2.442188e+01 1.538281e+00
## [76] 2.522488e+01 4.736206e+00 2.279325e+01 6.644105e+00 9.293664e+00
## [81] 2.555348e+00 1.532520e+01 7.575239e+00 1.313072e+01 2.296309e+00
## [86] 4.846901e+00 8.531091e+00 1.025610e+01 8.598807e+00 3.033722e+01
## [91] 6.010361e+00 6.297441e-01 8.075657e+00 1.261471e+01 3.396082e+00
## [96] 3.610513e+00 9.323502e+00 2.443124e+00 1.609964e+01 2.310390e+00
## [101] 1.457877e+01 6.337539e+00 2.332425e+00 5.179497e+00 3.972643e+00
## [106] 2.292647e+01 5.237968e+00 6.306357e+00 3.414498e+00 2.267203e+01
## [111] 2.496742e+01 6.415429e-01 1.434429e+01 1.577429e+01 2.252292e+00
## [116] 3.227622e+01 1.135725e+01 1.139550e+01 1.611917e+01 1.468025e+00
## [121] 3.650329e+00 1.611311e+01 1.263648e+01 5.277850e+00 5.512857e+00
## [126] 8.221396e+00 1.001873e+00 3.371936e+01 2.853532e-01 4.271252e-01
## [131] 2.761274e+01 1.786843e+01 3.289628e+00 1.188893e+01 2.689864e+01
## [136] 6.619067e+00 1.194223e+01 2.957747e+01 3.246399e+00 3.055162e+01
## [141] 1.527055e+00 1.557468e+00 1.319385e+01 1.855555e+01 6.145435e-01
## [146] 1.879637e+00 1.079863e+01 1.067482e+01 1.869794e+00 1.033521e-01
## [151] 9.579388e+00 1.650172e+00 8.782397e+00 3.596966e+00 1.148193e+01
## [156] 1.494377e+01 8.332578e+00 8.879959e+00 3.204514e+01 1.062161e+01
## [161] 1.923582e+01 5.863126e+00 3.346318e-01 3.382006e+00 4.413296e+01
## [166] 2.873570e+00 7.278469e+00 1.156956e+01 8.768428e+00 4.888542e+00
## [171] 1.533562e+00 1.005907e+01 1.454045e+00 2.311852e+00 1.679506e+01
## [176] 1.561556e+01 2.123980e+01 3.405872e-01 2.106276e+01 7.753798e+00
## [181] 2.788697e+00 6.062907e+00 1.699296e+01 1.960377e+01 4.848661e-01
## [186] 9.499509e+00 3.188840e-01 3.453398e+00 6.058758e+00 4.698690e+01
## [191] 1.092194e+00 5.650985e+00 3.574745e+00 6.287887e+00 1.341329e+01
## [196] 1.239223e+00 4.904959e+00 2.259063e+01 6.535519e+00 3.717386e-02
## [201] 3.307320e+00 1.944305e+01 6.075307e+01 8.659862e+00 5.130770e+00
## [206] 5.143413e+00 1.782096e+01 4.683111e+00 1.576407e+01 6.823170e+00
## [211] 1.295739e+01 1.505788e+00 3.506352e+01 1.287992e+01 4.556745e-01
## [216] 1.899627e+00 2.456436e-01 1.327700e-01 2.328074e-01 1.274467e+01
## [221] 5.635927e+00 3.816699e+00 4.401645e+01 2.129782e+01 4.861720e+00
## [226] 1.592131e+01 1.366593e+00 2.557678e+01 8.964024e+00 3.625314e+00
## [231] 2.288124e+00 2.517645e+00 1.059122e+01 6.689281e+00 4.092245e+01
## [236] 9.221529e+00 5.635943e-01 8.692540e+00 1.520396e+01 2.882644e+01
## [241] 1.667175e+01 3.301003e+01 2.850120e+01 4.182966e+01 2.291423e+01
## [246] 7.569664e+00 1.366006e-01 1.447909e+01 7.636259e+00 2.946664e+01
## [251] 1.988615e+00 3.193398e+01 1.695142e+01 5.704824e-01 1.172150e-01
## [256] 3.247524e+00 8.286802e+00 2.944894e+00 1.429432e+01 1.768474e+01
## [261] 4.451199e+00 1.003420e+00 1.524661e+01 2.490336e+01 1.620710e+01
## [266] 2.489595e+01 3.235636e+01 6.882170e+00 1.291546e+00 3.524543e+00
## [271] 1.123201e+01 3.653306e+00 8.776463e+00 1.103139e+00 7.506828e+00
## [276] 1.606501e+01 6.898882e-01 2.838920e+00 2.687077e+01 5.066306e+00
## [281] 4.259395e+00 1.706844e+01 7.012497e+00 3.552830e+00 3.630483e+01
## [286] 8.916262e+00 1.534570e+01 2.469332e+01 1.115191e+01 2.182615e+01
## [291] 1.203588e+01 1.083498e+01 3.974962e-01 4.808702e+00 4.906199e+00
## [296] 4.759186e+01 6.035666e+00 1.353884e+01 1.338984e+00 8.694888e+00
## [301] 2.966406e+00 1.816766e+01 4.258693e+01 2.418180e+01 3.029515e+00
## [306] 2.528996e-01 1.561427e+01 1.366505e+01 1.317208e+01 3.365799e+01
## [311] 2.602020e+01 7.222135e+00 8.619141e+00 7.736154e+00 9.000687e+00
## [316] 1.385632e+01 3.018813e+01 4.792794e+00 5.176100e+01 1.447646e+01
## [321] 1.227655e+01 6.352789e+00 1.673285e+01 1.691111e+00 1.087573e+01
## [326] 1.888867e+01 1.092173e+01 1.085378e+01 1.833185e+01 8.462746e-01
## [331] 4.224069e+00 2.022561e+01 7.015063e+00 1.815897e+01 1.071544e+00
## [336] 5.769938e+00 7.244742e+00 1.827307e+01 2.078796e+01 3.657148e+01
## [341] 7.284969e+00 2.412231e+01 5.705521e+01 5.696106e+00 2.666539e+01
## [346] 7.360443e+00 3.279591e+01 4.063603e+00 9.376402e+00 1.036001e+01
## [351] 1.884146e+00 4.366688e-01 2.439634e+00 1.033481e+01 1.446150e+01
## [356] 5.728584e+00 3.464600e+00 5.919975e+00 4.218553e+00 1.117871e+01
## [361] 1.306782e+01 5.649834e+00 5.149163e+00 4.717368e+00 9.773980e+00
## [366] 1.034973e+01 3.296811e-01 2.518704e+01 4.637549e+01 3.591721e+01
## [371] 4.635612e+00 4.945342e+00 4.285084e+00 3.873337e-01 2.726982e+00
## [376] 2.863610e+01 2.480531e+01 8.738404e-01 7.870483e+00 9.708237e-01
## [381] 2.362551e+00 4.079307e+01 2.463892e+01 5.773727e+00 6.930485e+00
## [386] 8.010623e-01 4.051276e+01 1.021314e+01 1.047708e+01 4.005776e+00
## [391] 2.415953e+01 7.249245e+00 2.495605e+01 2.332340e+01 2.864992e+00
## [396] 5.131678e+01 1.481656e+01 1.479876e+01 3.801615e+00 2.535753e+01
## [401] 2.288485e+01 1.004613e-01 2.258626e+01 6.209879e+00 1.742769e+01
## [406] 1.206541e+01 4.418374e+01 1.325529e-01 2.829256e+00 1.803824e+00
## [411] 5.687308e+00 9.667490e+00 2.927963e+01 4.520159e+01 1.844981e+01
## [416] 1.133777e+01 3.860453e+00 8.464821e-02 1.344789e+00 1.604152e+01
## [421] 3.168790e-01 2.373085e+01 6.782858e+00 1.985099e+01 1.714535e+01
## [426] 2.058771e+00 1.904679e+00 4.591147e+00 6.288812e-01 4.970683e-01
## [431] 4.336693e+01 2.107430e+01 7.353201e+00 1.141805e+01 1.340975e+01
## [436] 6.635491e-01 1.440916e+01 1.206721e+01 1.582713e+01 1.009685e+01
## [441] 1.770516e+00 1.680064e+00 8.991389e+00 2.098860e+00 3.868913e+00
## [446] 1.028576e+01 5.443176e+00 1.165966e+01 7.707863e+00 1.302747e+00
## [451] 1.191251e+01 7.765504e+00 7.872707e-01 2.671734e+00 7.699208e+00
## [456] 1.455825e+01 9.931254e-01 3.938846e+00 2.360692e+01 1.571785e+01
## [461] 4.407430e-01 2.051332e+01 8.911555e+00 1.246976e+01 2.375861e+00
## [466] 1.978588e+00 8.763495e+00 8.559752e+00 3.520661e+00 9.356772e+00
## [471] 6.884970e+00 6.350541e+00 4.155551e+00 9.369417e+00 8.224918e-01
## [476] 1.682972e+00 1.935589e+01 5.605045e+00 5.517039e+01 4.305837e+01
## [481] 7.514922e+00 4.190781e+01 1.222830e+01 1.528842e+00 2.631737e+01
## [486] 7.797657e+00 1.185441e+01 1.389191e+01 2.513934e+00 4.087769e+01
## [491] 1.872132e+01 7.329366e+00 5.709677e+00 1.190779e+01 1.434239e+01
## [496] 3.841858e-01 2.744485e+01 2.012026e+01 3.359822e+00 6.208104e+00
## [501] 1.148275e+01 1.071556e+01 1.431330e+01 5.278299e+00 2.815899e+00
## [506] 1.415290e+01 4.323100e+00 5.408292e+00 4.888149e+00 2.958378e+01
## [511] 6.993261e+00 1.013112e+01 8.286084e+00 3.242355e+01 5.988121e+00
## [516] 5.978838e+00 8.943698e+00 1.332651e+00 1.374885e+01 2.219561e+01
## [521] 1.517897e+01 1.133920e+01 1.502889e-01 1.940966e+00 4.460085e+00
## [526] 6.521267e+00 8.726466e+00 1.368981e+01 3.612590e+00 2.515974e+00
## [531] 9.319154e+00 1.054961e+01 4.149920e+00 3.684283e+00 2.018338e+01
## [536] 6.727056e+00 8.327417e+00 2.058464e+01 4.508435e+00 2.662836e+00
## [541] 7.892912e+00 1.119332e+01 1.018044e+01 1.248835e+01 5.533906e+00
## [546] 3.571425e+00 3.101689e+01 1.677597e+00 4.634246e+00 3.848588e-01
## [551] 1.458683e+01 6.127928e+00 5.630625e-01 5.047679e+00 2.776218e+00
## [556] 1.940903e+01 8.610859e+00 3.284698e+01 9.033258e+00 5.810593e+01
## [561] 6.278496e+01 9.632125e+00 7.097142e+00 1.366593e+01 3.464389e+01
## [566] 6.106211e-01 1.973515e+01 3.612622e+01 9.081169e+00 2.742749e+00
## [571] 8.012848e+00 6.400407e+00 3.781601e-01 2.082140e+00 1.839208e+00
## [576] 2.443369e+01 1.367147e+00 7.605434e+00 2.523568e+00 9.335783e+00
## [581] 1.366901e+01 5.584476e+00 4.361764e+00 1.507677e+01 2.332323e+01
## [586] 7.918881e-03 4.153934e+01 6.433323e+00 1.492940e+01 5.065276e+00
## [591] 5.884734e+00 4.668130e+00 5.385321e+00 3.343889e+01 1.475399e+00
## [596] 2.224243e+01 3.671499e+00 1.865837e+01 3.178436e+01 7.559945e+00
## [601] 1.151624e+01 1.806022e+01 1.175243e+01 1.805763e+00 1.517878e+01
## [606] 1.260125e+01 1.396558e+01 4.629327e+00 1.208971e+01 2.732760e-01
## [611] 1.985004e+00 1.710269e+01 1.275383e+00 1.718150e+00 9.208728e+00
## [616] 1.690181e+01 1.786424e+01 3.153457e+01 5.663808e-01 2.388748e+00
## [621] 2.868124e+01 9.555781e+00 3.874330e+00 1.414226e+01 4.048078e+00
## [626] 2.948299e+01 1.920916e+01 1.767809e+01 1.473060e+01 1.007805e+01
## [631] 5.597276e+00 1.455941e+01 2.281583e+01 1.079306e+01 1.221226e+01
## [636] 4.679047e-01 6.412772e+00 8.771038e+00 1.967827e+00 3.316614e+01
## [641] 2.377824e+00 3.689845e+00 1.584037e+00 4.443494e+00 2.930162e+01
## [646] 2.038048e+01 1.604096e+01 2.059308e-01 3.267696e-01 1.882487e+00
## [651] 9.965513e+00 1.750200e+00 3.442499e+00 3.376026e+00 1.451018e-01
## [656] 1.024397e+01 2.825707e+01 1.898317e+01 6.652645e+00 9.210009e+00
## [661] 1.518145e+01 1.472967e+01 8.116200e+00 1.797753e+01 1.466331e-01
## [666] 2.545563e+01 3.070518e+01 5.358013e+00 4.827721e+00 1.272377e+00
## [671] 1.718866e+01 1.091941e+01 1.210232e+01 1.377519e+01 1.298180e+01
## [676] 2.215793e+01 2.293480e+01 9.296910e+00 1.251351e+01 2.658016e+01
## [681] 1.422039e+01 1.678724e+00 1.007733e-01 3.423984e+00 5.824401e+00
## [686] 4.440372e+00 6.257072e+00 2.315874e+00 1.065623e+01 3.507512e+01
## [691] 9.003260e+00 3.099853e+00 9.443973e+00 1.547406e+01 1.769305e+01
## [696] 1.900097e+01 1.100555e+01 1.497239e+00 2.958783e-01 2.050310e+00
## [701] 3.125549e+01 3.955703e+00 2.602143e+01 2.450453e+00 8.047176e+00
## [706] 7.703376e+00 9.659807e-01 3.357286e+01 2.334622e+01 5.182023e+00
## [711] 1.493354e+00 6.885233e+00 8.195858e+00 9.888261e-01 2.588188e+00
## [716] 8.227500e+00 2.686186e+01 1.094905e+01 2.950183e+01 2.395442e+00
## [721] 4.336691e+00 1.965452e+01 1.464901e+01 1.735273e+01 3.198353e+00
## [726] 1.134099e-01 3.438425e+01 2.684391e+01 4.500923e+00 1.194185e+01
## [731] 2.858792e+00 3.602707e+00 2.795459e+01 4.485863e+00 7.693716e-01
## [736] 3.164170e+00 2.720442e+00 5.879056e+00 1.333488e+01 3.277687e+01
## [741] 4.679974e+00 2.210530e+01 3.928775e+00 3.041165e+01 2.234922e+01
## [746] 7.944389e+00 1.464665e+00 2.584139e+00 3.101156e+00 2.245591e+01
## [751] 2.690486e+01 2.934093e+00 9.647195e+00 1.313212e+01 3.159962e+01
## [756] 3.949847e+00 2.258832e+00 5.054935e+01 2.959697e+00 2.994179e+01
## [761] 3.116676e-01 2.082767e+00 9.331870e-01 8.715224e+00 1.189209e+01
## [766] 4.388546e+00 9.751120e+00 1.254366e+01 3.350511e+01 1.955439e+01
## [771] 1.650725e-01 7.940637e+00 2.713480e+01 6.302698e+00 5.051206e+00
## [776] 6.169507e+00 9.807604e+00 3.622140e+01 6.382870e+00 3.399793e+01
## [781] 1.024993e+01 3.135414e+01 1.055583e+01 2.392957e+01 2.133436e+01
## [786] 2.210793e+00 1.003108e+01 1.871800e+00 1.908772e+01 1.983314e+01
## [791] 4.543184e+00 3.450222e+00 2.781801e+01 1.835479e+01 1.580419e+01
## [796] 5.086104e+00 2.984039e+01 1.842839e+01 8.416092e+00 2.110104e+01
## [801] 3.764301e+01 2.771103e-01 1.518971e+00 1.555771e+00 3.854813e+01
## [806] 1.109906e+00 7.159562e+00 6.619758e+00 1.348109e+01 6.055768e+00
## [811] 1.347768e+01 1.566890e+01 5.144516e+00 4.768148e+01 5.525326e+00
## [816] 3.937319e+01 2.007827e+01 1.391834e+01 2.461331e+00 7.808185e-02
## [821] 1.299513e+00 1.827405e+01 9.388435e+00 5.425410e+01 1.598317e+00
## [826] 8.650627e+00 6.539908e-01 1.600363e+00 1.257718e+01 1.685332e+01
## [831] 2.032618e+01 6.421142e+00 1.817346e+00 3.344369e+00 1.227055e+01
## [836] 5.642871e-01 3.009076e+00 6.720884e+00 1.469730e+01 1.012764e+00
## [841] 1.902782e+01 6.209121e+00 5.477655e+00 6.891668e+00 1.592316e+01
## [846] 2.699053e-01 7.319827e+00 4.023091e-01 3.993227e+00 3.826179e+01
## [851] 1.038877e+01 2.714039e+01 9.975204e-01 3.233661e-02 7.768874e+00
## [856] 1.239684e+01 1.672443e+00 6.141898e+00 9.315068e+00 7.527416e+01
## [861] 6.628474e+00 1.191540e+01 1.414452e+01 1.981155e+01 1.607857e-01
## [866] 1.373376e+01 1.587266e+00 2.680637e+01 2.655513e-01 1.105475e+01
## [871] 4.148386e+00 7.537840e+00 1.355035e+01 1.392308e+01 1.623865e+01
## [876] 1.799516e+00 3.852920e+01 1.438936e+01 3.257973e+00 7.509046e+00
## [881] 1.598345e+00 1.417432e+00 5.883889e+00 8.099498e-01 4.374099e+00
## [886] 8.262175e-01 4.435890e+00 6.843735e+00 4.906295e+00 4.227473e+01
## [891] 8.202392e+00 2.234946e+00 2.924715e+00 3.383295e-01 2.367505e+01
## [896] 3.608065e+00 2.374316e+01 1.241960e+01 7.662020e+00 8.515708e+00
## [901] 4.688108e+01 8.796326e+00 5.208615e+00 2.621735e+00 2.915879e+01
## [906] 1.721018e+00 5.703111e+00 3.248330e+01 3.768709e+00 1.134205e+01
## [911] 8.870632e+00 4.191445e+00 2.117276e+01 1.404246e+01 8.463595e+00
## [916] 1.593021e+01 1.228919e+01 3.471963e+00 8.008751e-01 4.776439e+01
## [921] 6.100300e+00 3.997855e+00 3.170158e+00 1.014653e+00 1.209602e+00
## [926] 2.057675e+00 2.990058e+01 2.117528e+01 8.705785e+00 1.380318e+01
## [931] 3.292283e+01 3.145871e+00 2.867505e+01 2.319253e+01 2.392240e+00
## [936] 1.752696e+01 2.332342e+01 2.888610e+00 1.753497e+00 6.033770e+00
## [941] 1.460467e+01 9.229072e+00 1.576347e+00 2.014558e+00 3.058735e+01
## [946] 6.564740e+00 4.226148e+00 3.149499e+00 4.137494e+00 2.605955e+00
## [951] 1.071690e+00 2.509795e+00 9.110840e+00 2.814800e+01 4.324144e+00
## [956] 6.091134e+00 4.728578e-01 1.457114e+01 4.950560e+01 1.235466e+00
## [961] 1.473966e+01 1.204234e+00 1.564600e+00 5.948653e+00 1.473747e+01
## [966] 1.470071e-01 2.650947e+01 2.852000e+01 9.639736e-03 1.982655e+00
## [971] 1.637506e+01 1.205244e+01 5.005495e-01 1.702762e+01 2.776102e+00
## [976] 8.880429e-01 1.671017e+01 8.697633e+00 1.358543e+01 1.197496e+01
## [981] 3.214614e+01 3.581692e+01 9.889798e+00 7.814490e+00 2.986859e+01
## [986] 1.076104e+01 4.746157e+00 5.430133e+00 5.771707e+01 6.219115e+00
## [991] 1.458451e+01 1.086752e+01 1.339866e+01 2.525192e+01 2.049288e+00
## [996] 5.784878e-01 1.131321e+01 2.386204e+00 3.624829e+00 2.824081e+00
## [1001] 1.701442e+01 1.123359e+00 1.104479e+01 8.454148e+00 3.817703e+01
## [1006] 8.932685e+00 5.757304e+00 5.179510e+00 9.970116e+00 1.537800e+01
## [1011] 1.257779e+01 1.063357e+01 5.756591e+00 2.143319e+01 6.584001e+00
## [1016] 2.500263e+00 1.974269e+00 4.191156e+00 8.495168e+00 9.020556e+00
## [1021] 1.151025e+01 8.081133e-01 7.136140e+00 2.826428e+01 5.359516e+01
## [1026] 1.087753e+01 1.454427e+01 2.128218e+01 9.619508e+00 3.276875e+01
## [1031] 1.809645e+01 1.260251e+01 1.903856e+01 6.228384e+00 1.057791e+01
## [1036] 3.652128e+00 5.176567e-01 8.413681e+00 8.078071e+01 9.752972e+00
## [1041] 3.425977e+01 2.580985e+01 6.818424e+00 2.116964e+01 1.972584e+00
## [1046] 1.017021e+01 6.654951e+00 4.083933e+01 8.507902e+00 1.200061e+01
## [1051] 1.576914e+01 1.147524e+01 1.599795e+01 1.949625e+01 8.164850e+00
## [1056] 6.366358e+00 1.744661e+01 4.150668e+01 1.689763e+01 1.682848e+01
## [1061] 1.000070e+01 7.838245e+00 3.677053e+01 3.067505e+01 5.070380e+00
## [1066] 4.277070e+00 1.344991e+01 1.174238e+01 2.397420e+01 7.599366e+00
## [1071] 8.795219e-01 9.209304e+00 7.634798e+00 1.663190e+00 8.413628e+00
## [1076] 3.256903e+00 3.944100e+00 3.454893e-01 7.418753e+00 1.527859e+01
## [1081] 5.479980e+00 4.654585e+01 3.073435e+01 3.295709e+01 3.147999e+01
## [1086] 9.546545e+00 2.385313e+00 2.220024e+00 4.041722e+00 5.487669e+00
## [1091] 8.585029e+00 1.066572e+01 1.423894e+00 1.014335e+00 1.575275e+01
## [1096] 5.295051e+00 1.079559e+01 6.350333e+00 3.537721e+01 3.308747e+01
## [1101] 9.065252e+00 3.044302e+00 2.211254e+00 3.078505e+01 7.426741e+00
## [1106] 4.067321e+01 6.074201e+00 2.389753e+01 6.268219e+01 2.462086e+01
## [1111] 8.505102e-01 2.931811e+00 1.977715e+00 4.710876e+00 1.468882e+01
## [1116] 1.554204e+01 3.810948e+00 6.559618e+00 4.939709e+01 9.485558e+00
## [1121] 1.318091e+01 4.032777e+00 5.071581e+00 1.052454e-01 1.520015e+01
## [1126] 7.707532e+00 1.038321e+01 5.311727e+00 3.026100e+00 8.913988e+00
## [1131] 4.463864e-01 2.765170e+00 6.446452e+00 1.101676e+01 3.921952e+01
## [1136] 1.313790e+01 3.263165e+00 8.491596e-01 3.147334e+01 7.931005e+01
## [1141] 3.702421e+01 7.611549e+00 7.705251e-01 1.453181e+00 1.773375e+00
## [1146] 6.614608e-01 8.804287e+00 4.681421e+00 2.021652e+00 3.784910e+00
## [1151] 3.498627e+00 1.962517e+01 5.113835e+00 2.131729e+00 1.429821e+01
## [1156] 1.325180e+01 1.306583e+01 5.706176e+00 3.771436e+00 2.509427e+01
## [1161] 1.817823e+01 6.118569e+00 3.216274e+01 1.095145e+00 1.358739e+01
## [1166] 6.226818e+00 3.988659e+00 1.826625e+01 8.673661e-01 1.623649e+00
## [1171] 7.152886e+00 8.520347e+00 1.922273e+01 1.805271e+01 1.298566e-01
## [1176] 1.269428e+01 4.848915e+00 2.164957e+01 4.839751e+00 1.000762e-02
## [1181] 4.927461e+00 2.889221e+01 2.992994e-01 2.252464e+00 5.006492e+00
## [1186] 1.539196e+01 3.804075e+00 2.664472e+00 1.229369e+01 7.499006e+00
## [1191] 1.746569e+01 1.693974e+00 2.114556e+00 5.920142e+00 2.104686e+01
## [1196] 4.635643e+01 9.504052e+00 2.955518e+01 2.501681e+00 1.951324e+00
## [1201] 5.282591e-02 1.211295e+01 1.601853e+01 1.655098e+01 6.225847e+00
## [1206] 2.643141e+00 1.063057e+01 2.353450e+01 8.794382e+00 6.516632e+00
## [1211] 3.029371e+00 7.865298e+00 1.997480e+01 2.080082e+01 1.112811e+00
## [1216] 1.025757e+00 1.647992e+01 4.367041e+00 4.462466e+01 1.957541e+01
## [1221] 8.237438e+00 1.838686e+00 6.249168e+00 8.047232e-01 1.400466e+01
## [1226] 6.237561e+00 1.764268e+01 9.061572e+00 1.368745e+01 1.613407e+01
## [1231] 8.037781e+00 9.457431e+00 4.475121e+01 3.380388e+01 8.591649e+00
## [1236] 1.507599e+01 1.320941e+00 2.034093e+01 9.029676e+00 6.133040e+01
## [1241] 1.195227e+01 2.593045e+00 2.836748e+01 1.716470e+01 2.631343e-01
## [1246] 1.473547e+01 6.235836e+00 1.306855e+01 1.543647e+00 1.512537e+01
## [1251] 4.139783e+01 4.501642e+00 6.274735e+01 2.783990e+01 1.941762e+01
## [1256] 3.994317e+01 8.292795e+00 2.328307e+00 2.275204e+00 9.404194e+00
## [1261] 4.811975e+00 8.047708e+00 3.110833e+00 3.429929e+00 7.632167e+00
## [1266] 5.883324e+00 1.266747e+01 4.476474e+00 2.522315e+00 6.705521e+00
## [1271] 8.796994e-01 9.413433e+00 6.859977e+00 7.617711e+00 2.176173e-01
## [1276] 2.920901e+00 6.064570e+00 1.560980e+01 1.015716e+01 1.593551e+00
## [1281] 8.144677e+00 3.575727e+00 1.160937e+01 3.340199e+00 1.523124e+01
## [1286] 1.124513e+01 2.255374e+00 1.163014e+01 7.208888e-01 2.298618e+00
## [1291] 3.168507e+01 7.060737e+00 3.536215e+00 3.873784e+00 2.313481e+00
## [1296] 4.949585e+00 1.783110e+01 6.468352e+00 1.379508e+01 6.389509e-01
## [1301] 2.378363e-01 2.163236e+01 1.304467e+01 2.423321e+00 2.805189e+01
## [1306] 8.610345e-01 1.795031e+00 2.652730e+00 2.392523e+01 2.214675e+01
## [1311] 3.399047e+00 3.975256e+01 6.674252e+00 6.003963e+00 1.659082e+01
## [1316] 3.755162e+00 9.899032e+00 1.136813e+01 3.469950e+01 7.270944e+00
## [1321] 5.227124e+00 4.071509e+00 1.401564e+01 3.983819e+01 1.681107e+00
## [1326] 3.937026e+01 2.077973e+00 4.284524e+00 1.335408e+00 9.669500e+00
## [1331] 4.676745e+01 1.406280e+01 9.010973e+00 2.142108e+01 2.272948e+00
## [1336] 5.759779e+01 9.698933e-01 1.752368e+00 2.317601e+00 1.768470e+01
## [1341] 2.248160e+00 8.623896e-01 3.861664e+01 1.155310e+01 1.261086e+01
## [1346] 5.783918e+00 3.202934e+00 1.783870e+01 8.820980e+00 9.461676e+00
## [1351] 1.262663e+01 6.843619e+00 1.644650e+01 1.087295e+01 1.731298e-01
## [1356] 4.081881e+01 1.604316e+01 1.137941e+00 1.512442e+00 6.362244e+00
## [1361] 2.105274e+01 1.468396e+01 2.245710e+00 1.006384e+01 1.025110e+00
## [1366] 2.172647e+01 2.935916e+01 7.413970e+01 2.742140e+01 2.813617e+01
## [1371] 2.060571e+01 8.809605e+00 1.360898e+00 7.198772e+00 2.920152e+01
## [1376] 9.010587e+00 6.697851e+00 5.542210e+00 1.800750e+01 1.662596e+01
## [1381] 1.997908e+01 7.076488e+00 1.667186e+01 2.116214e+00 1.066031e+00
## [1386] 9.461373e-01 1.054930e+01 5.409682e+00 9.802153e+00 3.782034e+01
## [1391] 5.016474e+01 4.690137e+00 2.047190e+01 1.171459e+01 5.836495e-01
## [1396] 2.741786e+00 3.086534e-02 7.377426e+00 3.550852e+00 2.853081e+01
## [1401] 3.108317e+01 1.011551e+01 1.354713e+00 6.223575e+00 2.002572e+00
## [1406] 4.580097e+00 2.467673e+01 2.845331e+00 2.362220e+01 9.760851e+00
## [1411] 6.792632e+00 2.429436e+00 8.924494e-01 3.026475e+00 2.572710e+00
## [1416] 1.978703e+01 1.285022e+00 8.875981e+00 1.061421e+01 1.589256e+00
## [1421] 1.264599e+01 1.616411e+00 9.105411e-01 4.991726e+00 1.001225e+00
## [1426] 1.349782e+00 6.062012e+00 6.267721e+00 1.065968e+01 1.762048e+01
## [1431] 8.908096e-01 1.009640e+01 2.364147e+00 9.501316e-01 1.684451e+01
## [1436] 3.741736e+00 2.225964e+01 1.686061e+01 2.493861e+00 6.333679e-01
## [1441] 4.600865e+00 1.463617e+01 1.621705e+00 1.884010e+00 2.890680e+00
## [1446] 1.420128e+01 7.182541e-02 3.511682e+00 1.195095e+01 8.986062e+00
## [1451] 1.112800e+01 1.394455e+00 3.783892e+00 7.680980e+00 7.095012e+00
## [1456] 2.573699e+01 9.839458e+00 4.407446e+00 4.200074e-02 3.146053e+01
## [1461] 2.950853e+01 6.158143e+00 9.961150e+00 1.023092e+00 8.202098e+00
## [1466] 1.776065e+00 6.967824e+00 1.590411e+01 1.140165e+00 1.200580e+01
## [1471] 2.193114e+01 5.369841e+01 1.752545e+01 1.166369e+01 4.685042e+00
## [1476] 9.713117e+00 1.117910e+01 1.310483e+01 1.133050e+01 7.928599e-01
## [1481] 3.780835e+00 3.740297e+00 5.468849e+00 1.252094e+01 8.719317e+00
## [1486] 1.810437e+00 5.636902e+00 2.420168e+00 4.139610e-01 8.212923e+00
## [1491] 1.457420e+01 1.024768e+01 3.746323e-01 2.236578e+00 6.445825e+00
## [1496] 3.130654e+00 4.614156e+00 5.260741e+00 2.656387e+00 9.131458e+00
## [1501] 5.674296e-01 3.175019e+00 3.444343e+00 7.052250e+00 3.988908e+01
## [1506] 6.867506e+00 5.276736e+00 3.584336e+00 4.357546e+00 1.254070e-01
## [1511] 1.003796e+00 4.229027e+00 3.718618e-01 6.472031e+00 1.511347e+01
## [1516] 2.347276e+01 3.068311e+01 4.926865e+00 1.496204e+01 5.794536e+00
## [1521] 1.198213e+01 4.262688e+00 1.476607e+00 4.288672e+00 1.604514e+01
## [1526] 1.956130e+01 1.094069e+01 2.287255e+01 4.675261e+00 3.910771e+00
## [1531] 3.964897e+00 7.991836e+00 9.559351e+00 3.526341e+01 2.626040e+01
## [1536] 9.434381e+00 5.616248e+00 3.325284e-01 7.633205e+00 3.967684e+00
## [1541] 1.337341e+01 5.329077e+00 2.044504e+00 2.491633e+00 7.897779e+00
## [1546] 2.742161e+01 8.456673e+00 1.166522e+01 3.203309e+00 2.268381e+00
## [1551] 1.078417e+01 9.822933e+00 6.031478e+00 1.165613e+00 1.637997e+01
## [1556] 1.388380e+01 7.699506e+00 1.858485e+01 1.457965e+01 8.055617e-01
## [1561] 8.518283e-01 4.907710e+01 1.635665e+01 1.381562e+01 7.282803e+00
## [1566] 1.605764e+01 2.596847e+00 3.823943e+00 2.118719e-01 1.121284e+00
## [1571] 3.648815e+01 8.384610e+00 1.499698e+01 1.751195e+01 1.631417e+00
## [1576] 1.543197e+01 1.538732e+01 8.949065e-01 1.234045e+00 2.194928e+01
## [1581] 2.215123e+00 5.481545e+00 1.787672e+01 2.056538e+01 1.201824e+01
## [1586] 2.201461e-01 1.123619e+01 1.501029e+00 2.923470e+00 3.125377e+01
## [1591] 1.381917e+01 9.107070e+00 1.616249e+01 9.112844e-01 1.427519e+01
## [1596] 7.834343e+00 8.249624e+00 1.880364e+01 1.309805e+01 1.443311e+01
## [1601] 7.988533e+00 1.343131e+00 8.222582e+00 5.754992e-01 3.840204e+01
## [1606] 3.140080e+00 2.431291e+00 9.244078e+00 4.996380e+00 1.383059e+00
## [1611] 4.023240e+00 2.553162e+00 7.600986e+00 7.872611e+00 6.895488e-01
## [1616] 1.550285e+00 1.019265e+00 4.437031e+01 9.392970e+00 7.674514e+00
## [1621] 2.712378e+00 1.136231e+01 8.561576e+00 1.502726e+00 2.641643e+01
## [1626] 1.378467e+01 1.219155e+01 9.183494e-01 2.237639e+00 1.117246e+00
## [1631] 1.057811e+01 1.384489e+00 2.640237e+01 4.559693e+00 1.076670e-01
## [1636] 2.863932e+00 1.265378e+00 2.077332e+01 4.349883e+00 4.116022e+01
## [1641] 2.082148e+01 1.960442e+00 1.330373e-01 5.631624e+00 3.348664e+00
## [1646] 8.800223e-01 4.359495e+01 6.353189e+00 9.395273e+00 5.321786e+00
## [1651] 2.588039e+00 1.298864e+01 2.522455e+00 2.051370e+01 1.627711e+00
## [1656] 5.253653e+00 5.344461e+00 4.710493e+00 2.474550e+00 9.004801e+00
## [1661] 3.824616e+00 2.312689e+01 1.313653e+01 1.641973e-01 3.598217e+01
## [1666] 1.182647e+01 9.497854e+00 1.898533e+00 1.853064e+01 3.620733e+00
## [1671] 9.969007e+00 3.782042e+00 6.505140e+00 2.083982e+01 2.132712e+01
## [1676] 8.731056e+00 7.121970e+00 6.804893e+00 4.693470e+00 1.249502e+01
## [1681] 6.433916e-01 3.293072e+00 1.457875e+01 2.069273e-01 2.956088e+00
## [1686] 2.188319e+00 1.204441e+01 3.064239e+00 4.664953e+00 5.796333e-01
## [1691] 1.311075e+01 1.532503e+01 1.159792e+01 1.201335e+00 1.134028e+01
## [1696] 1.033774e+00 1.540178e+00 1.995565e+00 4.735300e+01 7.135735e+00
## [1701] 1.098113e+01 1.569077e+01 8.558148e+00 7.153160e+01 5.106731e+00
## [1706] 1.158521e+01 2.101768e+01 3.400546e+00 9.628006e-01 1.529241e+00
## [1711] 2.846755e+01 1.345815e+01 4.301146e+00 1.455942e+01 3.290011e+00
## [1716] 6.671139e+00 5.593124e+00 1.418638e+01 1.277672e+00 1.750799e+01
## [1721] 1.848939e+01 1.166998e+01 8.824757e+00 1.308683e+01 1.789384e+01
## [1726] 2.146312e+00 1.593931e+01 1.950519e+00 4.190608e+00 3.516790e+01
## [1731] 2.549417e+00 6.516371e+00 1.918666e+00 3.011638e+00 8.304332e+00
## [1736] 1.697919e+00 3.037729e+00 2.271275e+00 3.858094e+01 8.689606e-01
## [1741] 1.823131e+01 2.432773e+00 2.291997e+00 1.937049e+01 6.061531e+00
## [1746] 2.527314e+01 1.125826e+01 2.511589e+00 3.110972e+00 3.401840e+01
## [1751] 6.993311e+00 2.791718e+00 6.811743e+00 1.052263e+00 7.847615e+00
## [1756] 2.791172e+00 1.179613e+01 2.581326e+01 3.321580e+01 2.275250e-01
## [1761] 7.765863e-01 8.585751e-01 2.953682e+01 1.905397e+01 3.685711e+01
## [1766] 2.314127e+01 1.493016e+01 6.984535e+00 2.421830e+01 4.649543e-01
## [1771] 6.383648e+00 7.042258e+00 2.927373e+00 1.972935e+00 2.323282e+01
## [1776] 2.688205e+00 1.431236e+01 2.422263e+00 9.509267e-01 6.331276e-01
## [1781] 6.651213e+00 1.436005e+00 1.612877e+01 3.570901e+00 1.684678e+01
## [1786] 1.121975e+01 6.363872e+00 2.829589e+00 1.846222e+00 3.974486e-01
## [1791] 4.636117e+01 1.353470e-01 2.864862e+01 3.078564e+00 1.113066e+01
## [1796] 2.749681e+00 8.009755e+00 1.211942e+01 9.430974e+00 1.300115e+00
## [1801] 3.515917e+01 1.270444e+01 7.676673e-01 1.414149e+01 1.956237e+01
## [1806] 1.858410e+00 3.268308e+00 1.174205e+01 1.207905e+01 3.892786e+01
## [1811] 3.689298e+01 5.584582e+00 3.819371e+00 6.938725e+00 1.952262e+01
## [1816] 2.959874e+00 6.532718e+00 1.060847e+00 1.358563e+01 5.869710e+00
## [1821] 5.369056e+00 1.666522e+01 1.205595e+01 2.735435e+01 2.629613e+01
## [1826] 1.091701e+01 2.986584e+00 1.731415e+01 1.645809e+01 1.239111e+00
## [1831] 6.189227e+01 1.025405e+01 4.475516e+00 4.914412e+00 5.447110e-01
## [1836] 1.275116e+01 1.558261e+01 2.944653e-01 1.404877e+01 1.864668e+00
## [1841] 3.282044e+00 1.381535e+00 3.457606e+00 9.558565e+00 1.365013e+00
## [1846] 1.643725e+01 7.532392e+00 3.115218e+00 3.898424e+01 3.393995e+01
## [1851] 6.951675e+00 3.107711e+00 2.738254e+00 2.840366e+00 6.610180e-01
## [1856] 1.098744e+01 2.239996e+00 1.981225e+01 6.030966e+00 1.763118e+01
## [1861] 1.201728e+01 1.369624e-01 1.351890e+01 2.301797e+00 1.871345e+01
## [1866] 5.564915e+00 1.155098e+01 9.345903e-01 1.156149e+01 1.061445e+01
## [1871] 1.825237e+01 7.226504e+00 3.273237e+01 1.112403e+01 3.557396e+00
## [1876] 1.184386e+01 7.361969e+00 6.639652e+00 1.298724e+01 1.207190e+01
## [1881] 3.553355e+01 4.772489e+00 1.191735e+00 1.410271e+01 1.829385e+01
## [1886] 1.742700e+00 3.213785e+00 3.846635e+01 1.984146e+00 7.055368e+00
## [1891] 1.729541e+00 1.065731e+01 9.975546e-01 6.057624e-01 2.720873e+00
## [1896] 3.569545e+00 7.204275e+00 4.543129e+00 8.164790e+00 8.632865e+00
## [1901] 5.385797e+00 2.613206e-01 1.121494e+01 1.046696e+01 1.705799e+01
## [1906] 8.086812e+00 2.544449e+01 4.427956e+00 2.226120e+01 5.978431e-01
## [1911] 4.533195e+00 1.432709e+01 1.166939e+01 9.756141e+00 6.921395e+00
## [1916] 6.145426e+00 3.049047e+01 6.003976e+00 1.115911e+01 2.137393e+00
## [1921] 5.680952e+00 1.829837e+01 9.515861e+00 2.575969e+01 1.370649e+01
## [1926] 1.400468e+00 1.101303e+01 1.891058e+01 2.736802e+01 1.945068e+00
## [1931] 3.821304e+00 5.225024e+00 1.249554e+00 4.588933e+01 5.093276e+00
## [1936] 6.481077e+00 1.179713e+01 1.437988e+01 2.712369e+01 3.243871e+00
## [1941] 3.777906e-01 1.049346e+00 1.013556e+01 1.200294e+00 6.257717e+00
## [1946] 3.487506e+00 3.001895e+00 5.758931e+00 1.777628e+01 1.838708e+01
## [1951] 1.091427e+01 3.076568e+01 3.582921e+00 1.713870e+01 1.036946e+01
## [1956] 1.038332e+01 3.992904e+00 4.779657e-01 1.081841e+01 2.115091e+01
## [1961] 6.706358e+00 3.785991e+00 2.576630e+01 1.950886e+01 6.871211e+00
## [1966] 1.401986e+01 3.958758e+00 2.351763e+00 4.530707e+01 3.269330e+01
## [1971] 6.140065e+00 8.748933e+00 7.622989e+00 1.411172e+01 1.130942e+00
## [1976] 1.591481e+01 6.117202e+00 1.203724e+01 8.002517e-01 9.003637e+00
## [1981] 2.566701e+01 6.400275e+00 2.487216e+00 7.850886e+00 1.719965e+00
## [1986] 1.307443e+01 1.181082e+01 1.566413e+01 2.496873e+01 6.347117e-01
## [1991] 6.024586e+00 2.557993e+01 7.536067e+00 5.933572e+00 1.128987e+01
## [1996] 4.814999e+00 1.178532e+01 8.142347e+00 9.002289e+00 1.423507e+00
## [2001] 3.571889e+00 4.666014e+00 3.881747e+01 1.562762e+01 3.428988e+00
## [2006] 3.517063e+00 3.772593e+00 1.369183e+00 1.108653e+01 1.191814e+01
## [2011] 9.696421e+00 3.271814e+00 3.624526e+01 1.322502e+01 2.621566e+01
## [2016] 1.921131e+00 8.399391e+00 3.153832e+01 1.008931e+01 3.074115e+01
## [2021] 7.695859e+00 1.157105e+01 2.923260e+00 7.383313e+00 1.031767e+01
## [2026] 2.839348e+01 1.569743e+00 4.484276e-01 1.367517e+01 5.106967e+00
## [2031] 4.182185e+00 2.282815e+00 6.413891e+00 3.482617e+00 1.030483e+00
## [2036] 1.082838e+01 6.179666e+00 2.223126e+01 5.367231e+01 1.392231e+01
## [2041] 1.758019e+01 1.991249e+01 6.605225e+01 1.050412e+01 1.531660e+01
## [2046] 3.222793e+00 1.367925e+01 4.588960e+00 2.748973e+01 2.340741e+01
## [2051] 8.311977e+00 3.627479e+00 1.105329e+01 1.543944e+01 1.879009e+01
## [2056] 5.999480e+00 7.090226e+00 1.079276e+01 1.670672e+01 3.549999e+00
## [2061] 7.583292e+00 1.487781e+01 2.472596e+00 2.364492e+01 3.653914e+01
## [2066] 7.228155e+00 1.034371e+01 3.172528e+00 5.988072e+00 4.306473e-01
## [2071] 3.724306e+00 1.781041e+01 1.798004e+01 1.125941e+01 1.143074e+00
## [2076] 1.639081e+01 1.821277e-01 4.545432e+00 5.465363e+00 1.095998e+01
## [2081] 9.411928e+00 1.515180e+00 1.587241e+00 1.514175e+01 7.456434e+00
## [2086] 7.598599e+00 2.553844e+01 2.242770e+01 7.458278e+00 2.017731e+00
## [2091] 2.906785e+01 8.031848e-01 6.906467e-01 1.065513e+01 1.192279e+01
## [2096] 7.250344e+00 8.937519e+00 3.029770e+01 3.880447e+01 1.330418e+01
## [2101] 3.050980e+01 4.239353e+00 8.682577e+00 8.364308e+00 5.443661e+00
## [2106] 2.511221e+00 2.399700e+01 3.317285e+01 1.368446e+01 5.279673e+00
## [2111] 1.022702e+01 1.996445e+01 4.095116e+00 2.790173e+01 1.713613e+00
## [2116] 1.357359e+01 1.205711e+01 8.354719e+00 4.439838e-01 7.357750e+00
## [2121] 3.652273e+01 4.132267e+00 3.289174e+01 2.453896e+01 4.880111e+00
## [2126] 2.442953e+00 1.264910e+00 2.277485e+01 1.641862e+00 1.914707e+01
## [2131] 6.330134e+00 1.679054e+01 2.018377e+01 1.957268e+00 6.250913e+00
## [2136] 6.395406e+00 3.727121e+00 8.428359e+01 2.337206e+01 1.778004e+00
## [2141] 1.580485e+01 1.732418e+01 1.133555e+01 3.463857e+00 3.898500e+00
## [2146] 6.000427e+00 3.055763e-01 1.123160e+01 1.326349e+01 2.038781e+01
## [2151] 6.425502e+00 2.380851e+01 1.427078e+01 2.141815e+01 4.780425e+00
## [2156] 8.670167e+00 9.206877e-01 1.959487e+00 3.954693e+00 3.871602e+01
## [2161] 3.274596e+00 1.679770e+00 1.264077e+00 8.945374e+00 1.530642e+01
## [2166] 3.184820e+00 1.736166e+01 4.011663e+01 2.008084e+00 4.217829e+00
## [2171] 4.299346e+01 1.309779e+01 4.706618e+00 9.641446e+00 1.585601e+01
## [2176] 3.721782e+00 1.019982e+01 1.662909e-01 6.174581e+00 2.763252e+00
## [2181] 2.463617e-01 1.233808e+00 2.064244e+00 3.307138e+00 2.336496e+01
## [2186] 8.878602e+00 1.083627e+01 1.757951e+00 1.065564e+01 7.056324e+00
## [2191] 9.682865e+00 1.259078e+00 1.255190e+01 1.755251e+00 1.865798e+01
## [2196] 5.005239e+00 1.701267e+01 7.146832e+00 2.065689e-01 2.637499e+00
## [2201] 1.004951e+00 1.181838e+01 5.010834e+01 8.998769e+00 7.695219e+00
## [2206] 1.687263e+00 6.645205e+00 3.215533e+00 1.391368e+01 4.987653e+00
## [2211] 3.197390e+01 1.898588e+01 1.601550e+01 1.072092e+01 2.792744e+01
## [2216] 1.942859e+01 1.409671e+01 5.754708e+00 1.324170e+01 6.735002e+00
## [2221] 2.994179e+00 6.484028e+00 1.512427e+00 3.644388e+01 4.786353e+00
## [2226] 1.514127e+00 5.146944e+00 1.427395e+01 6.269805e+00 1.311051e+00
## [2231] 6.782672e+00 1.517253e+00 1.978221e+00 9.895907e+00 1.091030e+00
## [2236] 1.449482e+01 7.890496e-01 9.809860e+00 4.493389e+00 8.076024e+00
## [2241] 1.606627e+01 1.335358e+01 5.032928e+00 1.181778e+00 3.143649e+00
## [2246] 7.496897e+00 3.850776e+01 4.222735e+01 1.266436e+01 7.829778e-01
## [2251] 4.449477e+00 2.254509e+01 1.639960e+00 4.094194e+01 1.539974e+00
## [2256] 3.409984e+00 3.677598e+00 3.288347e+01 7.605344e+00 1.455196e+01
## [2261] 1.225512e+01 6.680427e+00 1.093829e+01 1.334097e+01 9.784802e+00
## [2266] 5.239117e+00 9.234276e+00 5.344534e+01 8.930444e+00 1.390049e+01
## [2271] 8.272832e+00 5.470967e+00 4.594829e+00 3.473651e+01 5.343983e+00
## [2276] 4.182053e+00 1.999778e+01 8.124130e+00 2.271071e-01 5.011187e+00
## [2281] 4.403670e+00 1.645684e+01 1.226940e+01 1.563099e+01 1.516536e+01
## [2286] 1.373381e+01 7.862068e+00 1.207051e+01 1.627777e+01 7.978086e+00
## [2291] 1.379056e-01 1.507781e+01 2.372083e-01 1.128937e+01 2.128283e+00
## [2296] 1.731683e-01 9.679389e+00 1.631842e+01 1.242392e+01 5.013488e+00
## [2301] 1.719958e+00 8.551862e+00 3.191422e+01 1.942431e+01 1.439979e+01
## [2306] 2.272960e+01 1.465348e+01 1.323777e+01 8.924459e-01 7.623056e+00
## [2311] 1.854729e-01 2.272177e+01 4.426122e+00 5.904824e-01 1.851893e+01
## [2316] 1.200273e+01 3.177200e-01 1.049798e+01 3.945273e+01 5.934173e+00
## [2321] 6.585108e+00 7.948686e+00 2.510504e+00 3.875924e+00 9.405330e+00
## [2326] 1.114538e+00 7.791538e+00 6.125168e+00 3.764299e+00 4.150352e+00
## [2331] 1.389930e+01 2.788118e+01 1.972823e+01 1.063569e+01 1.870903e+01
## [2336] 5.869388e+00 1.548768e+01 4.588591e+00 1.724401e+00 2.098520e+01
## [2341] 7.319665e+00 1.058317e+01 5.244327e+01 2.856169e+01 2.041598e+00
## [2346] 8.445943e+00 2.023017e+01 2.597136e+01 3.644769e+00 2.784958e+01
## [2351] 1.637180e+01 2.645542e+00 1.311462e+00 4.014978e+00 2.835986e+00
## [2356] 3.999625e+00 4.876683e+00 4.473771e+01 6.079612e+00 4.139634e+00
## [2361] 1.867358e+00 5.680161e+00 1.291368e+01 1.426589e+01 1.891127e+01
## [2366] 1.433475e+01 3.515973e+00 1.532710e+01 1.737063e+01 1.830115e+01
## [2371] 1.909816e+00 4.858773e+00 1.191858e+01 2.660655e+00 8.969094e+00
## [2376] 2.966794e+00 9.617969e+00 6.137438e+00 5.359339e+00 1.013582e+01
## [2381] 5.828510e+01 1.319511e+01 2.322831e+01 4.374975e+00 1.447168e+00
## [2386] 1.554423e+01 3.615845e+00 1.370845e+00 1.198962e+00 4.326197e+01
## [2391] 1.919457e+00 1.266363e+01 2.148739e+01 6.992179e-02 4.552910e+01
## [2396] 6.853419e+00 8.297371e+00 1.168158e+01 1.556508e+01 2.145738e+00
## [2401] 7.493919e+00 1.605376e+00 2.624082e+01 3.817007e+00 1.602756e+01
## [2406] 8.869329e+00 2.239820e+00 1.543950e+01 5.071093e+01 9.197665e+00
## [2411] 1.411477e+01 1.110421e+01 3.553275e+01 2.355627e+00 2.610396e+01
## [2416] 2.023564e+01 1.355953e+01 1.117888e+01 2.821199e+00 3.310604e+00
## [2421] 5.904710e+00 6.725006e+00 1.521822e+01 4.165290e+00 9.967521e+00
## [2426] 1.524616e+01 1.553916e+01 3.555312e+01 2.358686e+01 9.931377e-01
## [2431] 9.026475e+00 3.989055e+00 4.208840e+00 5.110807e+00 9.655303e+00
## [2436] 1.067905e+01 7.133204e+00 2.474048e-01 3.104583e+01 1.013676e+01
## [2441] 1.323526e+01 7.426096e+00 8.049854e+00 7.590560e-01 3.536178e+01
## [2446] 1.323114e+01 3.663986e+00 2.145048e+01 5.509172e+00 8.085723e-01
## [2451] 4.303700e+00 3.340934e+00 1.802712e+00 4.648821e+00 1.008871e+01
## [2456] 5.811269e+00 1.192820e+01 1.967533e+01 1.094919e+00 1.812183e+01
## [2461] 1.897605e+01 1.317646e+01 4.675318e+00 2.295961e+01 1.018708e+01
## [2466] 8.322937e+00 4.260499e+00 2.400578e+00 2.370040e+00 2.501653e+01
## [2471] 8.023620e+00 4.102627e-01 1.042974e-01 6.362981e+00 3.413303e-01
## [2476] 8.105143e+00 2.840047e+00 5.499472e+00 3.673887e+01 4.577512e+00
## [2481] 1.824790e-01 2.830968e+00 8.596549e+00 3.254098e+01 4.036252e+00
## [2486] 1.343403e+01 4.180437e+00 7.484306e+00 1.291731e+01 5.040453e-01
## [2491] 1.484393e-01 3.252399e+01 1.856430e+01 3.382793e+00 4.413714e+00
## [2496] 2.669729e+00 1.731581e+00 5.693424e+00 1.993755e+01 2.960187e+01
## [2501] 3.028878e+00 2.511859e-01 1.962111e+00 4.237311e+01 6.511332e+00
## [2506] 1.472335e+01 9.806256e+00 1.246287e+00 1.052665e+01 1.022144e+01
## [2511] 6.334302e+00 3.920711e+00 1.167737e+01 2.068363e+01 1.534851e+01
## [2516] 2.289244e+00 2.572483e+00 1.377579e+01 1.717378e+01 1.776164e+00
## [2521] 2.652731e-01 4.859645e+00 1.972359e+01 9.135029e+00 1.155214e+01
## [2526] 9.906836e+00 1.552007e+01 4.713820e+01 2.232606e+01 2.347875e+00
## [2531] 1.389220e+01 5.932139e+00 7.726592e+00 2.968910e+00 2.269694e+01
## [2536] 1.308314e+00 4.526035e+01 2.386208e+01 1.563913e+01 1.697405e+01
## [2541] 9.771941e+00 1.487592e+01 6.582021e+00 2.211742e+00 5.192768e+00
## [2546] 1.878404e+01 4.637988e+00 6.437050e+00 6.663317e+00 3.531536e+00
## [2551] 1.250395e+01 1.255857e+01 8.988559e+00 9.782457e-01 4.685002e+00
## [2556] 2.091288e+01 3.734546e+01 1.048697e+01 8.084783e+00 2.467407e+00
## [2561] 2.096799e+00 8.086966e+00 2.798481e+00 2.683639e+01 4.220008e+00
## [2566] 1.453176e+01 4.689198e+00 1.767849e+00 1.800161e+01 5.873280e+00
## [2571] 7.471385e+00 8.914987e+00 4.711684e+01 1.938447e+00 3.422235e+00
## [2576] 1.335481e+01 9.165642e-01 1.064305e+01 7.968452e+00 2.170010e+01
## [2581] 1.116963e+01 1.347767e+01 9.452813e-01 1.072912e+01 1.236124e+01
## [2586] 1.320803e+01 6.008354e+00 1.139287e+00 9.069474e+00 2.222143e+01
## [2591] 5.607399e+01 3.275035e-01 3.212746e-01 7.774013e+00 4.954948e+00
## [2596] 9.430289e+00 1.117560e+00 1.100400e+00 6.405693e+00 5.400441e+01
## [2601] 2.596852e+01 1.690396e+01 7.636003e+00 1.061028e+01 2.443601e+01
## [2606] 1.473589e+01 2.709408e+01 5.628104e+00 1.169628e+01 7.700262e+00
## [2611] 1.170401e+01 8.112242e+00 1.341333e+01 1.718150e+01 1.013109e+01
## [2616] 1.941197e+00 3.618850e+00 1.239951e+01 6.881683e-01 2.932653e+01
## [2621] 1.808966e+01 2.338195e+01 8.862680e+00 5.874332e+01 1.776681e+00
## [2626] 2.589438e+01 2.250859e+01 8.026034e+00 1.180979e+01 2.188197e+00
## [2631] 1.879311e-01 5.291907e+01 7.092591e+00 1.885514e+01 1.149876e+01
## [2636] 2.055051e+01 4.529223e+00 4.905073e+00 2.094570e+01 1.900698e+00
## [2641] 3.389271e+01 1.423402e+01 3.891544e+00 3.144450e+00 9.652532e+00
## [2646] 9.072072e+00 3.558766e+00 2.136958e+01 2.890494e+00 1.268740e+01
## [2651] 2.479814e+00 9.537262e-01 2.602469e+00 9.270498e+00 2.962688e+01
## [2656] 6.142738e-02 2.886863e+01 1.927752e+01 1.400429e+00 5.330615e+00
## [2661] 9.808322e+00 7.693347e+00 1.667515e+01 5.131421e+00 1.823451e+01
## [2666] 8.425592e+00 1.035628e+01 1.694196e+00 1.106505e+01 1.086161e+01
## [2671] 8.197272e+00 1.107103e+01 4.807371e+00 1.291700e+00 1.189856e+01
## [2676] 4.663770e+00 4.069413e+00 6.551685e-01 1.686281e+01 7.027970e+00
## [2681] 2.082588e+00 1.823939e+01 2.512964e+00 4.797627e+00 2.201878e+00
## [2686] 1.517290e+01 1.058421e+01 1.642809e+01 3.468803e+01 1.971448e+00
## [2691] 1.944183e+01 5.062849e+00 1.004419e+01 1.774107e+01 3.929254e+01
## [2696] 3.062379e-01 1.722036e+00 3.337723e+01 8.970120e+00 1.869609e+01
## [2701] 5.333554e+00 1.464958e+01 3.604433e+01 2.791283e+01 2.707465e+00
## [2706] 8.277813e-01 9.731039e+00 1.704074e+00 3.324586e+00 7.036391e+00
## [2711] 5.053984e+01 1.133897e+01 9.782575e+00 3.686304e+01 1.983756e+00
## [2716] 3.824896e+00 1.601707e+01 3.513643e+00 1.501862e+00 1.408809e+00
## [2721] 1.197442e+01 1.640896e+01 4.425332e+01 1.034818e-01 2.995386e+01
## [2726] 3.688828e+01 5.200228e+00 2.476436e+01 3.367918e+01 6.515120e+00
## [2731] 1.154192e+01 2.188882e+01 1.060811e+01 1.399078e+01 2.526954e+00
## [2736] 9.782839e+00 1.029843e+01 4.627028e+00 8.209538e+00 1.360797e+00
## [2741] 1.777615e-01 1.495357e+01 9.361039e+00 1.431925e+00 1.362253e+01
## [2746] 1.676016e+01 9.010101e+00 6.706679e+00 6.112658e+00 7.682218e+00
## [2751] 1.377693e+00 1.382333e+00 1.118523e+01 3.475180e+01 2.483894e+01
## [2756] 9.890627e-01 1.225264e+00 2.965732e+01 1.642455e+00 2.952319e+01
## [2761] 8.627937e+00 3.342960e+01 3.882525e-01 8.926651e+00 3.191430e+00
## [2766] 5.651166e+00 5.220108e+00 3.129215e+01 1.674184e+01 2.376484e+01
## [2771] 5.297997e+00 3.913712e+00 1.377373e+01 4.671624e+01 2.018713e+00
## [2776] 4.656356e+00 1.544595e+01 4.305534e+00 3.191984e+01 6.433260e+00
## [2781] 1.976117e+00 1.063709e+01 7.484258e+00 1.227426e+01 6.262068e-01
## [2786] 2.815361e+01 7.025787e-01 2.122518e+00 1.413991e+00 4.413736e+01
## [2791] 4.816863e+00 3.303592e+00 9.170707e-01 2.487757e+01 2.022937e+01
## [2796] 9.580573e+00 1.514791e+01 1.164178e+01 1.680271e+01 2.070640e+01
## [2801] 1.044534e+01 2.362438e+01 1.999349e+00 1.956686e-01 5.345873e+00
## [2806] 5.512560e+00 4.223076e+01 2.376988e+00 1.077446e+00 6.943385e+00
## [2811] 1.535707e+01 2.988322e+00 2.371723e+01 5.600135e+00 1.515739e+01
## [2816] 8.472439e+00 1.378555e+00 1.257160e+01 4.899723e+00 1.722098e+00
## [2821] 3.825207e+01 1.924910e+01 1.847172e+01 1.149848e+01 1.034693e+01
## [2826] 8.208190e+00 3.208977e+00 5.327801e+00 2.185464e-01 6.984485e-01
## [2831] 2.307535e+01 1.106007e+01 2.902454e+01 3.744313e-01 2.615498e+00
## [2836] 3.873625e+00 2.723329e+01 1.991978e+01 2.579801e+01 8.906128e-03
## [2841] 6.143715e+00 7.564881e+00 4.811369e+00 7.679284e+00 1.896400e+01
## [2846] 2.557354e+00 2.902620e+00 6.354706e+00 3.765957e+01 4.997535e-01
## [2851] 3.745679e-01 1.962865e+01 5.594823e+00 2.203334e+01 1.328703e+01
## [2856] 4.502418e+01 7.445645e+00 5.005763e+01 5.521194e-01 2.001126e-01
## [2861] 2.730210e+01 6.456025e+00 1.046592e+01 1.884588e+00 3.284376e+01
## [2866] 2.290636e+01 4.533727e+00 6.712873e+00 1.174797e+01 1.515195e+01
## [2871] 5.630146e+00 1.300527e+01 9.795197e-01 2.825714e+00 1.538635e+01
## [2876] 2.099406e+01 5.230752e+00 8.320630e-01 3.790458e+00 4.772288e+00
## [2881] 9.781881e+00 7.333296e+00 2.342162e+01 2.481922e+01 1.751435e+01
## [2886] 1.244917e+01 4.758002e-01 3.698791e+01 7.535674e-01 3.854260e+01
## [2891] 4.284808e+01 3.347837e+00 3.155977e+00 1.517433e+01 1.024141e+01
## [2896] 1.236334e+01 3.600459e+01 1.701108e+01 1.395665e+01 1.916164e+00
## [2901] 1.157282e+01 1.926027e+00 6.373169e+00 4.017959e+00 5.047799e+00
## [2906] 1.560978e+01 8.371271e+00 1.703120e+01 1.407279e+01 3.951990e+00
## [2911] 4.608253e+00 5.547147e+00 1.509240e+01 4.713685e+00 2.344621e+01
## [2916] 1.879742e+01 1.460993e+01 3.618939e+01 1.155448e+01 1.306496e+00
## [2921] 2.254787e+01 3.448572e+00 3.302765e+01 1.592208e+01 8.818481e+00
## [2926] 2.814537e+01 1.139992e+01 3.422529e+01 7.618689e+00 5.810274e+01
## [2931] 1.847588e+01 3.186165e+00 3.212873e+00 2.727655e+01 2.893369e+01
## [2936] 8.906657e+00 4.774101e+01 1.095379e+01 2.534620e+01 6.592466e+00
## [2941] 1.162576e+01 9.317693e+00 4.867593e+00 3.595056e+01 5.061666e+00
## [2946] 3.731426e+00 4.423053e+00 6.216233e+00 6.758750e+00 2.208329e+00
## [2951] 5.236631e+00 6.847973e+00 1.066646e+01 1.333150e+01 1.282712e+01
## [2956] 2.075348e+01 1.672431e+01 2.019492e+00 2.040100e+01 1.577162e+01
## [2961] 1.429570e+00 2.708811e+01 3.934529e+01 6.911417e-01 1.596966e+01
## [2966] 1.374353e+01 8.999068e+00 8.288093e+00 1.160585e+00 1.284154e+01
## [2971] 7.105977e+00 3.646822e+00 8.548066e+00 7.225408e-01 1.528683e+01
## [2976] 3.706877e+00 2.555230e+00 3.263618e+00 3.126532e+01 1.082334e+01
## [2981] 2.539700e+01 3.802160e+01 3.332421e+00 3.197164e+01 9.521559e+00
## [2986] 2.283568e+00 7.539076e+00 4.718014e+01 3.659239e+00 1.285969e+00
## [2991] 9.959221e+00 1.643945e+01 1.463164e+01 2.798304e+00 1.263133e+01
## [2996] 1.427207e+01 1.979049e+01 2.513314e-01 1.766200e+00 3.120655e+01
## [3001] 9.047471e+00 4.688491e+01 4.453577e+00 2.156118e+00 2.172846e+00
## [3006] 1.808429e+01 4.892280e+00 5.375991e+00 6.414720e-01 3.025510e+01
## [3011] 8.819092e+00 5.242946e+00 1.704547e+01 1.356885e+01 6.384648e+00
## [3016] 2.354802e+00 1.280560e+00 6.734126e+00 1.594935e+00 4.657363e+00
## [3021] 5.444531e+01 6.172623e-01 1.438037e+01 1.638147e-01 6.010050e+00
## [3026] 2.596425e+00 1.024463e+01 1.904041e+01 1.929797e+01 2.777489e+01
## [3031] 2.224403e+01 3.043296e+00 2.689204e+01 1.012860e+01 3.408874e+00
## [3036] 3.180869e-01 2.705910e+00 7.679456e+00 2.642926e+00 8.455516e+00
## [3041] 3.575198e+01 2.927098e+01 2.436282e+00 4.850511e+00 6.362031e+00
## [3046] 8.750495e+00 5.889847e+00 1.346006e+01 5.242868e+01 2.065379e+00
## [3051] 1.397729e+01 1.496092e+01 2.066944e+01 1.727750e+01 6.585309e+00
## [3056] 1.882490e+01 2.478324e+01 6.879390e+00 3.292844e+01 7.660196e+00
## [3061] 4.371135e+00 2.772409e-02 3.695290e+01 2.520906e+01 6.464896e-01
## [3066] 1.664236e+01 2.814039e+01 1.026012e+00 4.004887e-01 9.698401e+00
## [3071] 2.404468e+01 5.798868e+00 1.660789e+01 9.041632e+00 2.348286e+00
## [3076] 5.881390e+01 2.315149e+01 2.503686e+00 3.977475e+00 9.603862e-01
## [3081] 2.145793e+01 3.553244e+00 1.569958e+01 2.472804e+01 3.238271e+00
## [3086] 1.096281e+01 6.281638e+00 4.873750e+01 1.624523e+00 3.015246e+00
## [3091] 1.803696e+00 2.595521e+00 5.840790e+00 1.211625e+01 1.602354e+01
## [3096] 1.298608e+01 1.101100e+01 1.328505e+01 1.363845e+01 2.908336e+00
## [3101] 1.929795e+00 2.248924e+01 6.857658e+00 4.406628e+00 2.175633e+01
## [3106] 8.503691e+00 1.128993e+01 7.717545e+00 5.329701e+00 2.850877e+01
## [3111] 1.938743e+01 9.046726e-01 1.847912e+01 1.375488e+01 1.949908e+01
## [3116] 2.998744e+00 8.091062e+00 1.253277e+00 1.583512e+01 6.145154e+00
## [3121] 1.661215e+00 8.419270e-02 4.163721e+01 2.981715e+01 1.425265e+01
## [3126] 6.775614e+00 6.754786e+00 1.094402e+01 6.339190e+00 3.066173e+00
## [3131] 1.682130e+01 2.701067e+00 1.849716e+00 1.384883e+01 4.408951e-01
## [3136] 2.472239e+01 3.870750e+01 2.090986e+01 1.411760e+01 2.702283e+00
## [3141] 1.519432e+01 1.708976e-01 5.489463e+00 1.833585e+01 4.278418e+00
## [3146] 2.699894e+00 3.590646e-01 1.378649e+01 3.707798e+00 7.959311e+00
## [3151] 5.629762e-01 1.977162e+01 1.787352e+00 1.129061e+01 4.733685e+00
## [3156] 3.500886e+00 6.929866e+00 3.761172e+00 3.441508e+01 9.966178e+00
## [3161] 1.253916e+01 1.924838e+01 8.557798e+00 1.116728e+01 1.792957e+01
## [3166] 1.155552e+01 1.732444e+01 3.196732e+00 1.474911e+01 2.156844e+00
## [3171] 1.015580e+01 2.780174e+00 7.377097e-02 4.866149e+00 3.014635e+01
## [3176] 7.217342e+00 8.223874e+00 9.870403e+00 1.633351e+01 1.752867e+01
## [3181] 2.013289e-01 3.719730e+00 4.814450e+00 1.324326e+01 4.500281e+01
## [3186] 2.869575e+00 5.236931e+00 9.582953e-01 2.233652e+01 1.214255e+01
## [3191] 2.920893e+01 1.179644e+01 7.793787e+00 9.924324e+00 1.790173e+01
## [3196] 5.571355e+00 2.997187e+01 6.180377e+00 1.788525e+01 2.709366e+00
## [3201] 7.778748e+00 1.215589e+01 1.295948e+00 3.972569e+01 1.748816e-01
## [3206] 1.509037e+01 8.868566e+00 4.834349e-01 4.593348e+01 2.305458e+01
## [3211] 5.917548e+00 6.099867e+01 1.749354e+01 7.704332e+00 1.537045e+01
## [3216] 5.517353e+00 8.478708e+00 2.832776e+00 7.835555e+00 1.867091e+01
## [3221] 1.228035e+01 1.506986e+00 6.161834e+00 9.670711e+00 1.649752e+00
## [3226] 2.983031e+01 8.267235e+00 1.426689e+01 6.415169e+00 1.387917e+01
## [3231] 7.976020e-01 8.144052e-01 1.975877e+01 6.618636e+00 1.700960e+00
## [3236] 4.755203e+00 6.559287e+00 6.855223e+00 3.909902e+01 1.417118e+00
## [3241] 6.762650e+00 1.998912e+00 1.696898e+01 3.246951e+01 2.265512e+01
## [3246] 2.212876e+01 2.798451e+01 7.028450e+00 7.575485e+00 3.075348e+01
## [3251] 6.265086e+00 1.300618e+00 2.204940e+01 2.685700e+00 5.095779e+00
## [3256] 1.687163e+01 7.906037e+00 4.240080e+01 2.145363e+01 7.164086e+00
## [3261] 7.391204e+00 1.813572e+01 1.487122e+00 3.049545e+01 1.344692e+01
## [3266] 1.212185e+01 1.007435e+01 1.252321e+00 3.199686e-01 3.848517e+00
## [3271] 3.458083e+01 8.315443e+00 2.042522e+01 2.418676e+01 3.274580e+00
## [3276] 9.575795e+00 1.106723e+01 6.505779e-01 7.032665e+00 7.583330e+00
## [3281] 8.426055e+00 4.789955e+00 1.022518e+00 2.986210e+00 6.412953e+00
## [3286] 1.401922e-01 4.635213e+01 1.522242e+01 2.943382e+01 2.557916e+01
## [3291] 8.378640e+00 7.105843e+00 1.989025e+01 1.712482e+01 2.251214e+01
## [3296] 3.506096e+00 1.372110e+01 3.383023e+00 1.649026e+00 9.843567e-01
## [3301] 7.259995e+00 8.058702e+00 4.362162e+00 5.627876e+00 2.046361e+01
## [3306] 3.967110e+01 1.069166e+01 5.017194e+00 8.559077e-02 1.476649e+01
## [3311] 4.688775e+01 4.431856e-01 3.217728e-01 1.055929e-01 1.527872e+01
## [3316] 7.881656e+00 4.014119e+00 2.833066e+01 9.783960e-01 5.752282e+00
## [3321] 2.741377e+00 3.382610e+01 6.647845e+00 1.465491e+01 3.108604e-01
## [3326] 7.490997e+00 1.835114e+01 1.656699e+00 1.576351e+01 1.199737e+01
## [3331] 1.929524e+01 1.412659e+01 3.853977e+00 5.832394e+00 1.484198e+01
## [3336] 3.332835e+00 3.622444e+00 5.666776e+00 2.021336e+00 1.035154e+00
## [3341] 1.149965e+01 2.608082e+01 2.967393e+01 4.109390e+00 1.212437e+00
## [3346] 9.735094e+00 4.554060e+00 2.297831e+01 2.288266e+00 4.759878e+00
## [3351] 7.994059e+00 1.868971e+01 6.257829e-01 1.609620e+01 8.190514e-01
## [3356] 3.777153e+00 8.867638e+00 6.316609e+00 1.291404e+01 1.524870e+01
## [3361] 2.882238e+01 1.711577e+01 1.576009e+00 1.184850e+01 4.807662e+00
## [3366] 2.524275e+00 3.807047e+00 4.699068e+00 1.938118e-01 6.094656e+00
## [3371] 2.886199e+01 1.966770e+01 1.932475e+01 6.504809e+01 1.680509e+01
## [3376] 2.534988e+01 8.279976e+00 9.407225e+00 9.699685e+00 5.055375e+00
## [3381] 1.023268e+01 5.318960e+00 5.235614e+00 7.321255e+00 2.040015e+01
## [3386] 4.095892e+00 5.756350e-01 1.724696e+01 2.358327e+01 3.751004e+00
## [3391] 1.068213e+01 9.239000e+00 2.032074e+00 9.952566e+00 8.864984e+00
## [3396] 3.084477e+01 7.149427e-02 5.047435e+01 2.291512e+01 5.531925e+00
## [3401] 2.062796e+01 3.193410e+01 1.745633e+00 1.826990e+01 2.773304e+01
## [3406] 3.721310e+00 3.130635e+01 5.542982e+00 8.027169e-01 1.195259e+01
## [3411] 7.710275e+00 1.780366e+01 1.620347e-01 8.669837e+00 1.429129e+01
## [3416] 3.136591e+00 4.320884e+01 3.750809e+01 2.790309e-01 1.111390e+01
## [3421] 4.460335e+00 1.457595e+00 1.359362e+01 3.638299e+00 9.482656e+00
## [3426] 2.047253e+01 3.038149e+00 6.181337e+00 1.011636e+01 1.206987e+01
## [3431] 1.500132e+01 1.961480e+01 2.344866e+01 2.863576e+00 3.255110e+00
## [3436] 1.513649e+01 6.998326e+00 4.279575e+00 2.486582e+01 2.190582e+01
## [3441] 4.928279e-01 3.805569e+00 1.519314e+01 6.947205e+00 1.122064e+01
## [3446] 3.853720e+00 2.051966e+01 3.780350e+00 1.514326e+01 2.158018e+00
## [3451] 3.666843e+00 1.485872e+01 8.944728e+00 1.385095e+00 2.558097e+01
## [3456] 8.865264e-01 2.465866e+00 1.257916e+01 1.739834e+01 7.726627e+00
## [3461] 2.607276e+00 2.361010e+01 3.627048e+00 2.874766e+01 1.360084e-02
## [3466] 8.564925e-02 1.143721e+01 1.409194e+01 9.752513e+00 9.401670e+00
## [3471] 1.784528e+01 2.521003e+01 8.585342e+00 2.059757e+01 1.299144e+01
## [3476] 8.098334e+00 2.506954e+00 1.203772e+01 2.385688e+01 1.163547e+01
## [3481] 2.049593e+00 1.475293e+01 2.762583e+01 2.272764e+01 1.453925e+01
## [3486] 1.370727e+01 5.762805e+01 1.739197e+01 1.860865e+01 2.913823e+00
## [3491] 2.950088e+01 1.088910e+00 5.051579e+00 1.033540e+01 4.557984e+01
## [3496] 6.207144e-01 1.081946e+01 3.225416e+01 1.494772e+01 1.020489e+00
## [3501] 6.134815e-01 3.253121e+00 1.287212e+01 1.631395e+01 1.019621e+01
## [3506] 5.670577e+00 3.333790e+00 1.243787e+01 1.747069e+01 1.247508e+01
## [3511] 5.590407e-01 4.588080e+00 2.147680e+00 1.220356e+01 7.681274e+00
## [3516] 5.671836e+00 2.591694e+01 1.148928e+01 7.798838e+00 1.277237e-01
## [3521] 2.684331e+01 1.146015e+00 2.861674e+00 8.109876e+00 3.099703e+01
## [3526] 2.423844e+00 1.282187e+00 1.395062e+01 3.678032e+01 2.108922e+01
## [3531] 7.509240e+00 2.043838e+00 1.699435e+01 5.297573e+00 1.066266e+00
## [3536] 1.134552e+00 1.743180e+00 6.766236e+00 6.422081e+01 1.335333e-01
## [3541] 1.360658e+01 5.839832e+01 1.589237e+01 4.179369e+00 2.501289e-01
## [3546] 1.693969e+01 6.607700e-01 1.152296e+01 5.200104e-01 7.671763e+00
## [3551] 5.477945e+00 7.619398e+00 3.624269e+00 4.833702e+00 4.679424e+00
## [3556] 4.612219e+00 1.138972e+00 3.658671e+01 7.985818e+00 2.442761e+00
## [3561] 1.428545e+01 6.305604e+00 8.848626e+00 7.669237e-01 6.229733e+00
## [3566] 1.045076e+00 8.224092e+00 3.941482e+00 2.349843e+01 5.684416e+00
## [3571] 9.010821e+00 4.062188e+00 3.531816e-01 3.465200e+01 4.292562e+00
## [3576] 7.439106e+00 2.602210e+01 5.978469e-01 3.266719e+01 1.940001e+01
## [3581] 3.857372e+00 1.705793e+01 2.231584e+00 1.210702e+01 6.372553e+00
## [3586] 2.445268e+00 3.860090e+00 1.756348e+00 4.588372e+00 2.737846e+00
## [3591] 5.876497e+00 9.692722e+00 1.533888e+00 2.003611e+00 9.274224e+00
## [3596] 7.078334e+00 2.393136e+00 6.806936e+00 4.742147e+00 1.967733e+01
## [3601] 1.797129e+01 4.462114e+00 2.238907e+01 1.671105e+01 1.101722e+01
## [3606] 2.607720e-02 8.814069e+00 1.607432e+01 5.340263e+01 1.957636e+01
## [3611] 1.149083e+01 3.998319e+00 1.027021e+00 2.124228e+00 5.463999e+00
## [3616] 7.280251e+00 6.896806e+00 1.686527e+01 3.238341e+01 8.063688e+00
## [3621] 1.513682e+01 2.562644e+00 3.024390e+00 1.945827e+01 1.811838e+00
## [3626] 8.900246e+00 2.296948e+01 7.403799e-01 1.250067e-01 9.351992e+00
## [3631] 2.376865e+01 1.135830e+01 5.490646e+00 1.784469e+01 1.402505e+01
## [3636] 7.813713e+00 2.052836e+00 1.133792e+01 5.394152e+00 2.482506e+01
## [3641] 3.834331e+01 2.024646e+01 1.886712e+01 1.625120e+01 2.451168e+00
## [3646] 6.697717e+00 1.191802e+01 1.967560e+00 1.660897e+01 1.419895e+01
## [3651] 4.003171e+01 2.524264e+00 1.101448e+00 2.525266e+01 1.210099e+01
## [3656] 1.351243e+01 4.653795e+01 1.332752e+01 1.366337e+01 2.096924e+00
## [3661] 7.107013e+00 1.614219e+01 1.506148e+01 8.407716e+00 3.455063e+01
## [3666] 9.676730e+00 8.595452e+00 1.031525e+01 9.974574e+00 2.942704e+00
## [3671] 1.803193e+00 1.796819e+01 6.434309e+00 1.259299e+01 2.037840e+01
## [3676] 2.863894e+01 3.730128e+01 5.568121e+00 1.019199e+01 7.755538e+00
## [3681] 9.812891e+00 8.272160e+00 1.612601e+01 2.145753e+00 4.665852e+01
## [3686] 2.974295e+00 4.367776e+00 2.260018e+00 1.176776e+01 9.010384e+00
## [3691] 5.893531e+00 4.709019e+00 4.455009e+00 2.565564e+00 1.363287e+00
## [3696] 1.853612e+00 3.998035e-01 9.410704e+00 8.230128e+00 1.058454e+01
## [3701] 4.167676e+00 3.567518e+01 1.352732e+01 9.910186e+00 1.444851e+00
## [3706] 5.373639e+01 2.043631e+01 2.249906e+00 8.954979e+00 4.608899e-01
## [3711] 1.700375e+00 1.114813e+01 3.317920e+01 2.299309e+00 2.503253e+00
## [3716] 1.471059e+01 1.702140e+01 1.033432e+00 2.451848e+01 2.492256e+00
## [3721] 1.653031e+00 4.616769e+00 1.088679e+01 2.463426e+00 6.990888e-02
## [3726] 3.307223e+00 2.661736e+01 1.160817e+00 3.760148e+00 5.619494e+00
## [3731] 5.024804e+00 1.776433e+00 2.504726e-01 6.766617e+00 6.915046e+00
## [3736] 3.207713e+00 7.247896e+00 1.532898e+01 2.380633e+01 2.777562e+01
## [3741] 6.353542e+00 1.223819e+01 1.403320e+01 2.453727e-01 5.069604e+00
## [3746] 1.794451e+01 1.531839e+01 2.193037e+00 1.047674e+01 5.025558e+00
## [3751] 1.898957e+01 5.310465e+00 1.279960e+01 1.064655e+01 9.986622e+00
## [3756] 3.114675e+01 7.657009e-02 7.458922e+00 8.632704e+00 1.204387e+01
## [3761] 1.570172e+00 6.523417e+00 8.925577e+00 6.937904e+00 3.152140e+00
## [3766] 4.014748e+00 3.036697e+00 1.225003e+00 2.128888e+00 1.678385e+01
## [3771] 5.875809e+00 1.792033e+01 9.539419e+00 1.176403e+01 8.505780e+00
## [3776] 3.463443e+00 1.903692e+01 1.203125e+01 1.553761e+01 2.021518e+00
## [3781] 4.836808e+00 6.252232e+00 1.998929e+01 6.031460e-01 3.482734e+01
## [3786] 2.198435e-01 1.408626e+00 2.481487e+01 2.165256e+00 1.192349e+00
## [3791] 8.225872e+00 2.474800e+00 1.412582e+01 1.644002e+00 2.367687e+00
## [3796] 6.543075e+00 3.445743e+00 6.189329e+00 1.055206e+01 5.539611e+00
## [3801] 1.981645e+00 2.575074e+00 2.626764e+01 2.486548e+01 3.828073e+00
## [3806] 2.634778e+01 1.335546e+01 1.987932e+00 4.823873e+00 5.798679e+00
## [3811] 1.599869e+01 1.339834e+00 1.768581e+01 2.042146e+00 1.301641e+01
## [3816] 3.610260e+00 4.692738e+00 8.382844e-02 1.891836e+01 1.560779e+01
## [3821] 2.656976e+01 3.943597e+00 5.477145e-02 8.665518e-02 2.843540e+00
## [3826] 4.342790e+00 1.260175e+01 1.336628e+01 2.313764e+01 9.026455e+00
## [3831] 4.070406e-01 1.559352e+01 6.025327e+00 7.352343e+00 1.006903e+01
## [3836] 6.193027e+00 3.646962e+01 8.537159e-01 4.509182e-01 7.263016e+00
## [3841] 1.364776e+01 1.547022e+01 4.617233e+01 3.022288e+01 2.325614e+01
## [3846] 2.127746e+00 7.121539e-01 6.793642e+00 1.227675e+00 9.740842e+00
## [3851] 9.590670e+00 6.116314e+00 7.558816e-01 1.118631e+01 1.334109e+01
## [3856] 8.031482e+00 2.701776e+01 4.132721e+00 1.595391e+01 1.645316e+01
## [3861] 1.619502e+01 1.224907e+01 2.302463e+01 9.970729e+00 1.984204e+01
## [3866] 2.215297e+01 1.145513e+01 2.577872e+00 3.204041e+01 6.105046e+00
## [3871] 7.545143e+00 5.369821e+00 1.305626e+00 1.613770e+01 2.768993e+00
## [3876] 1.950444e+00 3.115137e+00 6.951064e+01 2.201975e+01 1.075733e+01
## [3881] 1.594584e+00 5.918007e+00 1.124489e+01 4.072828e-01 6.555748e+01
## [3886] 1.012713e+00 4.513602e+00 1.129447e+01 9.732977e+00 1.834543e+00
## [3891] 7.435764e+00 3.516367e+01 1.928829e+01 2.499062e+01 2.827431e+01
## [3896] 7.329262e+00 5.280193e+00 2.728776e+00 1.642111e+01 1.395370e+01
## [3901] 5.872436e+00 4.578845e+00 2.941133e+01 7.768869e+00 3.192531e+01
## [3906] 1.903711e+01 4.152648e+00 1.853818e+01 2.599625e+01 1.537068e+01
## [3911] 3.629391e+00 1.938451e+01 3.898585e+00 4.538122e+00 1.346688e+01
## [3916] 2.981567e+01 2.115413e+01 3.292828e+01 6.425724e+00 7.583629e+00
## [3921] 3.706422e+01 1.002930e+01 2.708861e+01 9.090685e+00 2.944082e+00
## [3926] 2.288332e+01 9.740191e+00 1.830889e+01 1.813928e+01 1.877437e+00
## [3931] 6.543566e-02 1.125847e+01 4.475071e+00 3.410476e+01 1.086015e+01
## [3936] 1.017760e+01 1.157868e+01 3.659135e+00 7.518538e+00 4.043894e+00
## [3941] 2.357974e+00 1.279330e+01 1.502263e+00 3.655278e+01 1.281041e-01
## [3946] 1.098382e+01 1.845471e+00 1.718141e+01 2.179670e+01 5.511601e+00
## [3951] 1.108166e+01 8.353205e-01 2.089020e+00 3.195694e+00 4.245186e+00
## [3956] 7.961016e+00 3.525764e+01 2.072045e+00 1.052070e+01 3.295902e+01
## [3961] 4.150558e+00 3.287753e+01 1.443695e+01 7.719115e+00 2.276476e+01
## [3966] 2.166800e+00 3.494399e+01 9.656598e-01 1.024351e+02 8.685599e+00
## [3971] 9.836997e-01 1.432835e+01 7.386202e-02 3.845515e+00 6.260394e+00
## [3976] 7.937239e+00 2.785860e+00 3.546489e+00 5.749048e+00 1.447091e+01
## [3981] 1.992052e+01 9.868150e-02 1.471860e+01 3.946294e-01 2.119066e+01
## [3986] 2.627790e+00 5.016726e+00 1.764757e+01 2.309803e+00 2.763130e+01
## [3991] 1.493828e+00 2.542865e+01 3.927062e+00 5.960247e+00 1.856564e+00
## [3996] 3.952122e+00 7.951299e+00 9.842201e-01 6.087284e+00 2.272497e+01
## [4001] 3.240467e+01 1.429708e+00 3.471614e+00 5.019364e+00 1.126650e+01
## [4006] 8.270270e+00 9.501744e+00 3.268445e+00 1.324393e+01 1.280834e+01
## [4011] 5.137965e+00 1.969678e+01 1.165056e+01 6.637376e-01 2.254648e+01
## [4016] 1.324741e+01 1.715329e+00 6.910529e+00 2.638154e+00 5.563750e+00
## [4021] 1.212871e+01 9.527748e+00 1.364972e+00 1.395709e+01 1.308037e+01
## [4026] 1.150953e+01 7.024340e+00 8.185815e+00 3.822699e-01 1.829502e+01
## [4031] 1.887653e+01 3.304272e+01 4.276741e+00 1.742627e+01 9.853871e+00
## [4036] 4.405653e+00 8.571549e+00 7.412895e+00 4.350011e+00 5.390167e+00
## [4041] 1.948755e+00 3.008606e+01 2.281531e+00 6.856551e+00 6.008749e+00
## [4046] 1.142685e+01 1.190751e+01 1.709417e+00 5.559819e+00 1.733441e+01
## [4051] 8.501664e-01 2.484102e+01 7.001174e+00 1.670369e+00 2.148443e+01
## [4056] 2.559746e+00 2.014989e+01 3.039055e+00 9.535594e+00 4.039386e+01
## [4061] 1.631730e+01 3.136842e+00 9.364360e+00 8.809893e+00 1.432309e+01
## [4066] 4.093111e+01 1.076408e+01 6.026977e+00 2.972929e+00 5.269022e+00
## [4071] 3.364905e-01 5.158815e+01 9.831799e+00 3.715040e-01 9.589995e+00
## [4076] 2.512910e+01 1.235738e+00 7.807065e+00 2.256721e+01 1.639766e+01
## [4081] 1.761042e+01 1.175560e+01 1.359260e+01 1.004026e+01 3.457756e+01
## [4086] 3.545515e+00 2.940939e+00 4.438842e-01 2.281520e+01 1.879698e+00
## [4091] 5.155539e+00 4.397929e+00 3.025043e+01 2.056011e+01 1.830892e+01
## [4096] 1.310517e+00 8.276461e+00 1.216432e+00 2.312671e+00 6.205249e+00
## [4101] 4.368193e+01 1.191977e+01 4.375762e+00 1.976603e+00 8.271083e+00
## [4106] 2.646266e+00 2.114489e+01 9.981384e+00 1.042180e+01 8.560914e+00
## [4111] 9.727933e+00 7.736226e+00 7.121507e+00 7.880674e+00 5.926504e-01
## [4116] 2.953655e+01 8.632300e+00 5.619303e-01 5.750024e+00 1.773271e+01
## [4121] 7.226189e+00 1.693607e+01 4.454222e-01 4.123038e+00 8.739975e+00
## [4126] 2.889411e+01 1.024273e+01 1.241499e+01 1.003772e+01 1.755930e+01
## [4131] 3.174731e+00 1.263381e+01 5.853732e+00 2.839397e+00 1.479596e+01
## [4136] 2.337799e+00 1.481534e+01 1.404347e+00 9.672565e-01 1.138454e+01
## [4141] 2.466856e+01 7.194311e-01 2.136790e+01 1.945482e+01 2.496494e+00
## [4146] 3.968479e+01 3.055472e+00 2.414386e+00 7.895636e+00 2.275635e+01
## [4151] 8.866868e+00 1.076021e+01 1.447561e+00 1.464677e+00 2.252114e+00
## [4156] 7.193176e+00 1.418676e+01 4.598336e+00 4.805369e+00 4.883435e+00
## [4161] 7.642751e+00 2.685126e+00 2.653858e+00 2.274293e+00 1.495196e+01
## [4166] 5.271346e+00 6.206094e+00 7.080443e-01 3.882460e+00 1.288187e+00
## [4171] 9.469486e+00 1.194956e+01 1.330673e+01 2.527780e+01 3.246320e+01
## [4176] 1.498114e+00 7.840600e+00 1.273176e+01 3.850659e+00 7.469707e+00
## [4181] 3.259771e+00 2.219091e-01 2.498613e+01 4.043643e+01 2.972883e+01
## [4186] 4.161199e+00 8.586047e+00 9.319853e+00 6.587086e+00 6.948730e+00
## [4191] 3.257569e+01 3.621162e+00 1.250088e+01 4.692194e+00 1.010476e+01
## [4196] 3.265234e+00 1.593489e+01 7.566827e+00 6.414460e+00 4.045806e+00
## [4201] 6.384319e+00 6.945053e+00 8.538761e+00 8.942667e+00 3.852220e+00
## [4206] 4.128326e+00 2.369511e+01 1.613354e+00 1.307282e+01 3.982855e+01
## [4211] 5.431034e-01 1.159590e+00 1.586455e+01 2.121204e+00 5.382989e-01
## [4216] 1.183666e+00 4.385548e-01 1.592336e+01 2.842241e+01 3.944092e+00
## [4221] 1.724871e+01 6.221870e+00 2.221487e+01 1.477140e+01 1.112965e+01
## [4226] 6.910465e+00 5.995577e+01 6.037620e+00 9.075849e+00 2.018447e+01
## [4231] 1.700826e+01 9.942997e+00 1.412991e-01 2.189185e+00 1.377300e+00
## [4236] 1.002473e+01 2.876666e+00 1.305030e+01 6.562192e+00 3.704322e+00
## [4241] 1.396563e+01 1.901544e-02 7.039221e+00 5.644237e+00 2.559662e-01
## [4246] 1.082563e+01 4.638600e+00 1.068638e+01 1.334005e+01 9.892457e+00
## [4251] 2.068057e+01 5.631845e+01 6.876274e+00 1.633848e+00 3.905871e+00
## [4256] 2.476158e+01 2.611628e+01 3.981529e+00 4.707491e+00 4.771916e+00
## [4261] 1.331401e+01 4.337247e+00 1.176970e+01 1.503504e+00 1.599315e+01
## [4266] 4.186698e-01 2.594183e+01 2.403314e+00 1.440258e+01 1.769519e+01
## [4271] 4.053034e-01 7.308947e+00 1.492018e+01 7.416483e+00 9.906989e-01
## [4276] 5.589178e+01 1.798565e+01 1.222196e+01 2.092839e+01 4.239327e+00
## [4281] 3.753303e+01 7.234156e+00 1.064406e+01 3.401147e+00 1.027885e+01
## [4286] 1.700903e+01 1.764814e+01 3.353763e+00 2.194601e+01 2.838500e+01
## [4291] 1.391448e+01 4.945407e+01 1.743095e+01 1.191580e-01 9.328804e+00
## [4296] 3.285100e+00 3.611759e+01 9.420761e+00 6.583403e+00 8.257578e+00
## [4301] 5.936354e+00 1.100052e+01 3.906524e+01 1.115732e+01 8.265476e+00
## [4306] 4.784974e+00 8.605853e+00 8.505315e+00 1.022791e+01 1.084868e+01
## [4311] 1.559622e+01 1.898058e+00 2.173166e+01 7.415809e-01 3.395240e+00
## [4316] 1.813971e+00 3.685954e+01 7.798696e+00 2.284398e+01 7.648429e+00
## [4321] 4.629474e+00 1.367112e+01 4.197614e+01 2.002997e+01 4.016076e+01
## [4326] 2.081781e+01 1.167115e+01 5.510125e+00 3.226943e+00 2.774225e+01
## [4331] 1.477037e+01 4.084936e+00 7.344671e+00 3.800196e+01 1.048112e+01
## [4336] 1.136601e+00 4.846635e+00 2.599650e+00 5.645869e+00 3.109746e+01
## [4341] 2.733986e+00 9.680854e+00 4.992738e+00 2.877402e+01 1.365846e+01
## [4346] 9.024291e+00 2.398812e+01 2.360093e+01 4.528514e-01 2.072944e+01
## [4351] 3.692706e+01 4.629644e+00 4.942021e+01 3.821583e+01 1.473666e+01
## [4356] 4.269804e+01 2.585320e+01 1.305280e+00 1.820259e-01 1.728153e+00
## [4361] 5.843306e+01 1.082524e+01 1.779623e+01 1.043934e+00 4.964270e+00
## [4366] 1.429403e+01 2.594040e+01 1.679842e+01 2.584606e+01 3.821449e+01
## [4371] 2.030883e+01 1.125094e+01 7.451083e+00 3.733643e+01 5.943698e+00
## [4376] 1.467148e+00 4.194461e+01 1.015056e+01 2.499415e+01 1.706540e+01
## [4381] 3.267983e+00 7.010501e+00 6.906429e+00 1.126674e+01 7.811966e-01
## [4386] 2.004539e+01 3.640992e+00 9.646675e-01 1.084018e+01 4.013258e+00
## [4391] 3.854609e+00 3.776957e+01 4.630413e+00 6.212384e+01 9.951793e+00
## [4396] 1.746689e+01 1.053051e+00 2.836253e+01 2.830269e+00 1.279309e+01
## [4401] 3.953519e+01 1.977569e+01 3.577299e+00 7.200697e+00 5.610147e-01
## [4406] 1.697388e+00 6.410524e+00 3.206021e+01 4.250372e+00 9.067992e+00
## [4411] 2.280906e+01 1.719945e+00 9.244999e+00 1.701691e+00 1.072330e+01
## [4416] 1.661127e+01 1.658695e+01 3.526766e+01 1.313311e+01 6.189817e+00
## [4421] 2.170925e+01 1.525155e+01 2.891833e+01 8.884260e+00 4.117596e+00
## [4426] 7.077326e-01 2.632938e+01 6.132355e+00 2.215117e+01 7.853176e+00
## [4431] 3.838995e+00 4.460441e+01 1.147767e+01 1.467600e+01 6.533917e+00
## [4436] 7.974722e-01 1.418686e+01 2.139294e-01 1.472871e+01 1.853985e+01
## [4441] 1.879550e+01 7.667581e+00 6.927886e+00 2.103239e-01 2.576166e+00
## [4446] 1.917815e+00 8.451880e-02 1.106762e+01 1.218029e+01 7.755969e+00
## [4451] 7.319739e+00 1.332653e+01 8.507342e-01 7.983037e-01 8.642339e+00
## [4456] 1.777942e+00 1.602474e+01 2.002508e+01 1.684101e+01 1.112855e+01
## [4461] 3.958625e+00 2.171249e+01 3.293830e+00 1.512357e+01 3.019304e+00
## [4466] 2.540015e+00 7.998440e+00 2.194006e+00 2.123324e+00 3.674092e-01
## [4471] 1.011837e+01 1.515103e+01 2.329151e+01 2.243192e+00 7.310241e-01
## [4476] 2.688980e+01 1.811855e+01 1.367116e+01 8.218539e-01 1.137327e+01
## [4481] 1.060733e+01 4.743214e+00 4.300559e+00 1.099570e+01 1.016648e+01
## [4486] 1.050657e+01 8.917077e+00 2.484181e+00 3.576136e+00 2.827535e+01
## [4491] 1.871663e+01 1.983904e+01 7.213198e+00 4.661509e+01 1.767553e+00
## [4496] 1.334265e+01 1.440228e+01 6.012446e+00 2.316419e+01 5.401878e+00
## [4501] 4.543639e+00 3.643563e+01 5.474593e-01 1.691551e+01 2.636651e+00
## [4506] 1.733998e+01 1.494154e+01 2.960426e+01 2.031964e+00 1.489051e+01
## [4511] 1.251736e+01 5.547635e+00 1.409783e+01 1.416990e+01 3.941703e+00
## [4516] 1.454906e+01 2.321252e+01 5.131403e+00 2.938172e+01 6.609158e+00
## [4521] 1.708444e+01 2.699209e+01 2.871884e+01 3.583103e+00 5.455409e+00
## [4526] 2.717578e+00 3.773258e+00 7.645040e+00 8.675558e+00 1.451790e+01
## [4531] 6.575518e+00 1.788837e+00 1.268107e+01 3.766568e+01 6.687797e+00
## [4536] 4.283576e+01 1.993276e+01 4.181690e+00 3.996722e+00 2.163056e+01
## [4541] 1.657520e+00 9.657861e+00 1.147259e+01 1.639484e+01 1.700015e+01
## [4546] 7.512597e+00 8.637062e+00 6.693793e+00 8.326029e+00 4.465428e+00
## [4551] 1.805566e+01 2.208809e+00 6.268647e+00 2.168742e+00 1.090599e+01
## [4556] 6.577671e-01 7.529647e-01 2.693829e+00 3.116506e+00 7.943108e+00
## [4561] 2.883028e+01 1.399420e+01 3.878586e-02 1.803845e+01 3.444624e+00
## [4566] 4.363822e+01 3.781415e+00 2.353969e+01 1.456077e+00 8.688435e+00
## [4571] 1.142450e+01 1.255208e+01 1.045390e+01 3.824609e+01 4.434003e+00
## [4576] 3.523379e-01 2.541511e+01 1.435612e+01 9.193243e+00 8.649213e+00
## [4581] 3.383090e+01 7.066363e+00 5.053888e+01 2.257542e+01 1.759979e+01
## [4586] 5.936992e+00 4.005580e+00 1.183482e+01 2.426894e+00 2.520388e+00
## [4591] 6.854358e-01 2.942621e+00 7.176077e+00 7.699781e+00 1.248003e+00
## [4596] 2.187553e+00 1.430905e+00 1.361112e+01 2.248699e+01 1.565902e+00
## [4601] 1.474657e+00 8.610837e+00 1.212599e+01 1.751492e+00 2.454580e+01
## [4606] 1.408998e+01 1.251853e-01 7.298773e+00 5.549608e+00 3.551274e+01
## [4611] 1.247311e+01 5.665353e+01 1.078865e+01 1.647949e+01 1.281816e+01
## [4616] 1.901334e+00 2.856150e+01 8.009655e+00 9.459934e+00 2.583815e+00
## [4621] 8.119554e+00 1.304193e+01 1.908777e+00 2.562789e+01 2.907023e+01
## [4626] 3.856379e+01 1.842980e+01 7.205870e+00 1.253586e+01 1.219425e+01
## [4631] 3.452820e+01 1.200498e+00 1.807906e+01 1.795714e+01 3.031085e+01
## [4636] 5.746650e+00 2.934003e+01 6.328609e+00 2.249624e+00 1.026338e+01
## [4641] 3.679726e+00 5.465946e+00 1.606794e-01 3.925379e-01 2.420848e+01
## [4646] 2.405626e+01 5.407796e+00 3.272601e-01 9.400677e+00 2.938282e+00
## [4651] 9.625763e+00 1.207420e+01 2.899581e-01 7.291424e-01 8.595919e+00
## [4656] 6.629077e+00 1.089489e+01 1.949071e+00 2.814015e+00 1.012924e+01
## [4661] 1.293002e+01 2.551777e+01 3.618147e+00 7.521983e+00 1.008446e+01
## [4666] 3.159357e+01 6.279160e+00 6.910027e+00 7.001617e+00 9.802093e+00
## [4671] 4.519925e+00 3.460037e+00 1.955714e+01 3.946018e+01 3.931770e+00
## [4676] 1.510471e+00 1.452035e+01 1.385408e+01 7.753074e+00 3.465399e+01
## [4681] 5.159240e+00 3.323960e+01 1.506735e+00 5.608943e+01 7.414551e+00
## [4686] 4.228196e+00 1.367654e+01 6.263460e+00 8.325031e-01 1.274488e+00
## [4691] 2.878849e+01 3.422980e+00 1.532697e+01 4.838743e+00 5.059070e+00
## [4696] 1.298389e+00 2.894498e+00 3.589263e+00 7.570810e+00 1.811609e+01
## [4701] 1.198548e+01 1.565390e+01 2.618979e-01 2.147071e+01 3.588106e+01
## [4706] 5.324362e+00 8.805114e-01 1.025052e+00 1.946561e+01 6.135322e+00
## [4711] 1.934012e+01 2.255554e+01 1.499951e+00 1.024992e+00 4.377625e-01
## [4716] 3.551879e+01 3.861437e+00 2.704053e+00 2.472404e+00 5.788566e+00
## [4721] 6.970966e+00 1.772240e+01 4.902174e+01 8.727196e-01 1.857913e+01
## [4726] 2.046340e+01 3.084522e-01 4.107549e+01 1.265246e+00 2.669000e+01
## [4731] 4.833506e+00 7.476313e-03 2.836306e+01 4.138567e+00 9.491824e+00
## [4736] 3.451184e+00 3.648265e+01 6.748070e+00 1.160676e+01 1.251880e+01
## [4741] 1.022463e+01 1.975866e+01 1.899525e+01 1.413408e+01 1.246720e+01
## [4746] 4.254768e+00 3.036039e+01 3.721514e+00 1.140298e+01 2.975524e+00
## [4751] 1.830584e+01 8.864767e+00 7.253275e+00 9.419293e+00 8.910336e+00
## [4756] 8.973868e+00 1.210158e+01 8.911762e+00 3.112075e-01 2.863312e+01
## [4761] 1.272132e+01 2.755998e+00 9.712949e-01 3.324803e+00 1.145444e+01
## [4766] 1.115014e+01 6.878994e+00 1.056110e+01 1.481126e+01 1.500086e+01
## [4771] 1.766488e+00 2.178535e+01 8.224429e+00 2.810777e+01 1.762736e+01
## [4776] 6.181326e+00 1.647501e+01 3.361434e+01 4.022034e-01 2.076634e+01
## [4781] 1.430125e+01 1.661085e+01 4.263294e+00 1.709578e+00 5.417614e+00
## [4786] 7.322219e+00 4.469167e+00 7.203475e+00 6.102711e+00 1.574193e+00
## [4791] 3.011706e+01 3.164704e+01 6.617984e+00 7.291450e+00 2.856629e+01
## [4796] 5.416390e+01 3.163834e+00 5.010092e+00 3.700018e+01 4.641213e+00
## [4801] 2.445304e+00 1.580301e+01 1.288485e-01 3.069706e+00 1.569227e+01
## [4806] 5.612301e+01 4.407914e-01 1.447677e+01 1.916827e+00 1.787299e+01
## [4811] 9.023140e-01 9.553069e+00 1.458838e+01 1.859905e+01 1.795040e+01
## [4816] 3.367420e+00 3.868089e+00 2.543455e+01 1.457003e+01 3.774852e+00
## [4821] 4.302176e+00 6.226727e+00 8.388490e+00 1.432699e-01 1.372778e+01
## [4826] 2.669420e+01 6.555787e+00 3.013258e+00 1.126053e+01 2.660376e+01
## [4831] 1.286356e+01 3.857696e+01 3.366004e+01 1.614479e-01 6.913670e-01
## [4836] 2.422535e+01 4.058137e+01 1.464124e+01 1.906147e+01 1.505483e+01
## [4841] 3.557266e+00 1.162134e+01 8.871143e+00 3.268981e+00 5.693428e+00
## [4846] 3.621932e+01 9.355883e+00 1.350461e+01 1.350872e+01 2.409212e+01
## [4851] 1.521592e+01 3.300131e+01 3.393890e+00 2.194958e+01 9.516996e+00
## [4856] 2.192536e+01 2.503260e+00 1.751411e+00 1.074507e+01 3.244768e+00
## [4861] 1.937052e+01 1.872871e+01 8.943176e+00 4.151038e-01 4.661329e+01
## [4866] 5.722657e+00 4.675370e+00 4.377336e+00 1.061481e+01 4.593674e-01
## [4871] 8.566673e+00 2.329875e+01 3.438131e+01 6.137210e+01 1.572829e+01
## [4876] 5.956381e+00 6.034605e+00 3.546964e+01 2.447583e+00 1.369639e+01
## [4881] 1.692472e+01 5.466136e+00 2.985195e+00 6.991362e+00 1.091784e+01
## [4886] 6.470311e-01 1.379404e+01 3.101490e-01 2.616256e+00 9.273491e-01
## [4891] 8.669895e+00 1.533256e+01 2.070529e+01 4.501103e-01 1.050824e+01
## [4896] 2.660488e+01 2.078709e+01 1.208215e+01 3.272882e+01 5.054334e+01
## [4901] 1.190306e+01 3.096660e-01 1.769537e+00 2.093881e+01 1.528466e+01
## [4906] 6.568551e+00 6.436855e-01 6.332332e+00 1.793426e+01 5.484373e+00
## [4911] 2.220008e+00 7.949117e+00 1.120500e+01 6.823440e+00 1.191213e+01
## [4916] 1.258802e+01 2.063046e+01 1.368874e+01 4.203563e+01 1.187929e+01
## [4921] 1.710029e+00 9.365116e+00 2.008212e+01 6.180738e+00 6.519392e+00
## [4926] 2.228811e+01 9.094343e-01 3.301066e+01 2.440609e+01 4.590309e+01
## [4931] 2.154787e+01 2.185442e+01 2.582404e+00 2.406339e+01 5.046978e+00
## [4936] 8.094175e+00 6.002199e+00 3.136853e+00 2.907895e+00 1.247095e+01
## [4941] 1.446142e+00 2.613575e+00 2.770017e+00 2.351293e+01 1.002270e+01
## [4946] 2.886050e+01 8.732799e-01 1.771448e+01 3.292058e+00 1.613387e+01
## [4951] 2.452379e+00 1.801293e+01 2.479333e+00 1.039827e+01 3.100686e+01
## [4956] 1.158349e+01 8.279310e+00 1.737472e+01 2.919476e+00 4.629031e+00
## [4961] 4.143185e+01 3.882953e+00 4.911778e+01 2.779133e+01 7.378826e+00
## [4966] 6.794400e+00 4.313500e+00 3.660705e-01 1.610909e+01 1.478781e+01
## [4971] 1.109876e+01 8.875074e-02 4.034058e+01 7.221057e-01 1.323038e+01
## [4976] 1.823505e+01 1.841088e+01 2.190658e+00 1.964589e+01 3.375699e+01
## [4981] 1.356364e+01 6.916889e+00 1.181816e+01 3.184598e+01 1.683434e+01
## [4986] 1.043206e+00 2.417892e+00 5.439092e-01 6.552998e+00 1.878127e+01
## [4991] 2.564136e+01 2.277516e+00 1.034181e+01 2.462488e+00 1.195886e+01
## [4996] 4.530593e+00 8.614686e+00 3.699251e+01 4.223738e+00 8.069831e+00hist(tiempoLlegada, main = "tiempo entre llegadas de solicitudes",col = "blue")
Interpretacion
En esta simulación de los tiempos entre llegadas observamos que la mayoría de los intervalos son cortos, cercanos a pocos minutos, y que los intervalos largos ocurren con menos frecuencia. Esto muestra en la grafica, donde la barra más alta está al inicio y luego va disminuyendo, lo cual es característico de la distribución exponencial con media de 12 minutos.
3. Duración de la atención
Cada ingeniero tarda en promedio 30 minutos en resolver un ticket, con una desviación estándar de 5 minutos.
A. Simule 5000 atenciones.
B. Grafique el histograma con la curva normal teórica.
C. Determine la proporción de atenciones que superan los 35 minutos.
set.seed(2804)
tiempoResolver<-rnorm(5000,30,5)hist(tiempoResolver, main = "Tiempo que tarda en resolver",col = "green",probability = TRUE,
xlab = "Minutos")
#Comando utilizados para hacer sobresalir la curva
xvals <- seq(min(tiempoResolver), max(tiempoResolver), length.out = 200)
lines(xvals, dnorm(xvals, mean = 30, sd = 5), col = "red", lwd = 2)
probabilidad <- mean(tiempoResolver > 35)
probabilidad## [1] 0.1596Interpretacion
En esta simulación vimos que los tiempos de atención se concentran alrededor de los 30 minutos, con pequeñas variaciones hacia arriba o hacia abajo, tal como lo indica la distribución normal. La grafica, junto con la curva teórica, muestra que el modelo se ajusta bien a los datos obtenidos. Además, se encontró que cerca del 16% de las atenciones duran más de 35 minutos.
4. Tickets escalados a segundo nivel
Un 20% de los tickets requieren ser escalados a un nivel superior. Suponga que en una hora se reciben 10 tickets.
A. Simule 1000 horas de operación.
B. Cuente cuántos tickets son escalados.
C. Grafique usando la función barplot.
set.seed(2804)
tickets<-rbinom(1000,10,0.2)
tickets## [1] 2 0 3 0 2 2 0 4 0 7 1 2 3 2 2 2 2 1 1 4 2 2 2 1 2 1 4 0 2 3 3 1 2 1 3 1 2
## [38] 2 2 1 2 1 4 3 4 4 1 1 1 5 4 1 0 2 3 1 3 2 3 2 3 2 4 1 3 1 3 2 2 2 2 2 3 2
## [75] 2 1 2 3 2 1 1 2 4 1 3 0 1 3 3 2 0 1 2 2 2 1 4 1 2 2 0 2 0 4 3 2 3 3 3 0 3
## [112] 2 3 6 2 2 1 3 2 0 0 3 3 2 3 4 0 2 3 1 2 3 1 1 3 1 2 2 4 2 1 1 3 0 1 2 2 2
## [149] 2 0 3 4 1 2 1 2 2 1 1 2 2 1 3 3 2 0 2 2 2 1 1 3 3 1 1 3 2 0 2 3 1 1 2 2 0
## [186] 1 3 2 0 1 1 3 2 2 1 1 1 3 1 3 4 2 0 1 4 3 2 2 2 5 1 1 1 2 4 2 3 2 2 0 3 1
## [223] 4 2 3 1 3 2 2 2 0 2 3 0 1 0 2 2 2 0 3 1 2 1 2 1 2 3 2 2 2 2 2 3 3 2 3 2 3
## [260] 2 1 1 1 2 2 3 1 2 1 2 1 2 3 2 1 3 1 2 3 4 3 2 2 0 3 4 5 1 1 1 4 2 3 4 3 1
## [297] 4 0 3 3 2 4 3 0 0 1 5 0 4 1 4 1 2 1 3 4 2 2 1 2 1 3 3 0 1 4 1 3 0 1 1 3 3
## [334] 3 3 5 2 3 2 2 2 2 4 3 1 1 3 3 2 2 1 3 1 2 2 1 3 1 3 4 1 0 3 2 0 2 0 4 2 2
## [371] 1 2 1 0 1 3 1 0 0 1 4 6 2 2 3 1 2 1 4 2 2 4 5 2 1 2 1 2 3 4 3 0 2 1 4 2 1
## [408] 1 2 2 2 1 2 2 1 2 3 2 2 4 0 4 0 2 2 2 2 4 0 1 3 2 0 2 1 1 2 0 1 2 3 3 2 3
## [445] 4 2 1 2 2 1 3 2 2 2 2 0 2 2 4 2 0 2 1 0 0 2 2 3 3 2 1 2 1 2 0 0 2 6 4 0 1
## [482] 0 1 1 1 1 1 2 3 4 2 3 2 2 4 4 2 1 2 0 3 2 4 3 1 1 4 3 1 2 2 2 0 1 1 1 2 0
## [519] 3 5 3 3 4 3 1 4 4 3 4 3 4 4 1 1 2 0 5 0 0 2 3 0 2 4 3 2 5 4 1 1 2 2 0 3 2
## [556] 3 1 1 3 2 5 1 1 2 3 4 3 1 2 3 2 0 1 0 0 1 2 4 1 4 3 4 4 3 2 1 0 1 3 0 3 0
## [593] 2 2 0 2 2 2 0 2 1 0 2 3 2 3 2 1 2 2 5 0 2 2 2 3 2 0 2 6 2 2 2 2 3 1 2 1 2
## [630] 2 2 2 5 3 1 2 3 2 3 3 1 2 0 3 1 1 3 2 1 4 3 4 3 3 2 2 1 3 1 5 5 3 2 4 4 2
## [667] 3 2 2 4 1 3 2 2 3 3 1 2 2 2 2 1 4 3 2 4 3 1 2 2 1 3 3 1 2 0 4 7 2 1 1 2 7
## [704] 2 2 1 1 2 2 3 0 2 3 3 2 2 3 2 2 2 3 3 2 3 3 1 1 1 2 3 0 4 3 1 2 4 2 0 3 1
## [741] 1 4 1 2 2 0 2 1 2 1 2 3 1 3 4 1 2 0 1 2 1 3 4 0 1 2 1 1 2 2 2 2 0 1 2 1 2
## [778] 4 1 2 2 1 3 3 5 3 1 2 0 0 0 4 1 4 1 1 3 0 0 1 0 5 2 1 0 2 1 0 2 1 1 2 3 0
## [815] 2 2 3 2 4 1 3 3 4 3 1 2 4 2 3 2 2 2 3 4 2 2 1 2 1 2 3 1 1 0 1 0 1 2 0 3 1
## [852] 2 3 1 1 0 1 1 1 2 2 2 1 0 3 1 3 2 1 1 4 1 2 2 2 0 1 4 3 2 1 0 3 1 1 3 1 2
## [889] 3 3 1 1 1 0 5 0 5 1 1 2 0 2 4 1 4 1 2 2 3 1 0 4 3 1 3 2 1 4 1 1 3 1 1 4 2
## [926] 0 1 1 4 3 2 2 4 2 2 1 0 2 0 1 2 2 5 2 1 3 3 3 2 2 0 2 2 1 2 2 2 1 0 0 4 3
## [963] 4 1 3 1 0 2 3 1 0 2 3 2 3 0 3 2 1 1 1 4 1 3 6 3 1 0 1 1 4 2 1 3 2 1 2 2 1
## [1000] 1sum(tickets)## [1] 1997barplot(table(tickets),
main = "Tickets escalados en 1000 horas",
xlab = "Número de tickets escalados en una hora",
ylab = "Frecuencia",
col = "orange")
Interpretacion
Al simular estas horas de trabajo observamos que, en promedio, se escalan alrededor de 2 tickets por hora, que es lo esperado con una probabilidad del 20% en 10 tickets. La suma de tickets escalados en toda la simulación fue cercano a 2000, lo que coincide con el valor teórico. El gráfico mostró que lo más común es que se escalen entre 1 y 3 tickets por hora, mientras que valores como 0 o más de 5 ocurren con menos frecuencia.
Conclusión
En base a las simulaciones realizadas en R se comprobó que las distribuciones de probabilidad permiten representar de manera realista fenómenos asociados al soporte técnico, como la llegada de solicitudes, los tiempos de espera, la duración de las atenciones y el escalamiento de tickets. Esto nos demuestra la utilidad de la simulación para analizar y comprobar el comportamiento de sistemas aleatorios y garantizar la toma de decisiones en contextos prácticos o comunes.