Taller Simulación de Variables Aleatorias
Rafael Yances
2025-09-17
Simulación de Variables Aleatorias no uniformes en R
Contexto
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.
Actividades
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.
# Distribución de Poisson con lambda = 5
set.seed(212)
llegadas <- rpois(5000, lambda = 5)
llegadas## [1] 4 7 6 3 1 2 8 8 4 4 5 5 7 3 3 7 6 3 6 8 5 5 6 0
## [25] 3 7 10 8 7 2 1 7 2 3 3 5 2 4 5 6 6 3 8 5 4 8 8 7
## [49] 2 2 3 4 3 7 5 5 4 3 5 4 5 2 5 5 8 9 7 4 6 10 4 8
## [73] 2 9 1 8 5 4 4 7 3 3 3 4 2 5 5 1 9 5 5 7 4 2 3 6
## [97] 2 4 10 7 3 7 3 3 5 5 8 7 7 6 2 5 7 3 4 4 3 6 5 4
## [121] 0 7 8 7 6 4 3 5 7 3 4 6 4 2 6 3 3 4 2 6 7 5 8 4
## [145] 4 10 3 4 5 7 8 5 2 5 8 8 9 5 6 5 4 7 4 6 7 10 2 6
## [169] 4 5 6 7 4 8 9 4 6 6 6 5 3 5 7 4 4 4 7 5 7 1 5 6
## [193] 4 3 8 5 3 5 4 5 5 5 4 4 6 2 6 3 6 4 2 3 5 4 10 7
## [217] 6 5 4 15 4 7 6 6 7 6 6 7 5 2 5 5 8 3 6 3 4 3 3 4
## [241] 10 7 5 3 7 4 7 5 1 7 2 6 3 3 11 7 8 6 6 7 5 5 8 5
## [265] 2 7 3 4 2 7 2 3 5 4 4 7 5 8 6 7 2 9 6 3 4 4 2 5
## [289] 3 2 1 7 6 7 4 5 5 1 4 9 4 5 7 5 5 7 9 6 3 4 5 6
## [313] 5 6 4 9 3 5 7 3 6 4 8 8 3 6 3 4 4 7 5 4 5 6 3 6
## [337] 5 4 8 6 2 2 8 3 6 6 4 8 9 9 7 9 5 5 7 1 4 5 7 3
## [361] 5 5 5 5 5 3 4 5 7 5 7 6 3 2 3 4 3 5 1 4 2 4 3 5
## [385] 2 3 4 4 10 3 4 4 1 8 9 4 5 9 8 9 7 5 3 2 6 5 6 2
## [409] 3 6 4 3 5 7 7 3 3 3 5 5 3 5 1 5 3 3 6 3 5 3 2 6
## [433] 6 5 8 5 5 4 13 3 8 1 5 2 2 1 8 3 4 3 3 9 5 4 8 3
## [457] 9 3 3 5 8 5 8 2 4 7 8 7 7 12 3 3 3 3 3 8 4 4 5 10
## [481] 6 6 4 2 10 4 7 5 9 5 10 6 5 5 4 4 7 6 6 6 6 5 6 6
## [505] 4 13 5 4 5 5 5 6 8 4 9 10 5 6 2 7 4 4 6 2 4 7 4 3
## [529] 3 5 8 3 7 7 4 4 3 9 2 4 9 1 8 4 8 6 10 5 7 6 6 3
## [553] 7 4 6 4 6 5 10 5 3 5 1 3 10 5 8 6 5 7 4 4 1 11 2 6
## [577] 8 4 2 14 10 3 3 6 7 4 4 9 4 3 8 2 3 6 6 4 2 7 5 8
## [601] 5 7 4 5 5 4 7 3 9 10 3 3 5 1 6 7 12 11 0 4 1 5 7 4
## [625] 7 3 5 6 5 5 3 4 3 11 5 3 8 5 8 5 2 4 5 3 3 6 3 4
## [649] 3 6 3 5 4 5 2 4 7 4 4 5 4 7 5 6 3 5 7 4 7 5 5 5
## [673] 6 1 5 5 2 3 8 6 7 7 7 6 6 7 2 5 7 3 9 6 4 3 8 4
## [697] 9 8 4 4 7 5 2 5 9 5 2 5 5 5 3 9 9 2 7 8 7 6 4 5
## [721] 6 1 5 3 2 2 2 4 6 5 1 3 1 7 5 4 3 4 1 6 1 7 4 6
## [745] 4 5 3 5 4 7 2 7 2 5 6 4 2 6 9 4 4 0 6 3 7 2 3 4
## [769] 8 5 4 5 5 5 4 8 3 3 1 8 6 5 5 2 6 7 4 1 3 1 6 4
## [793] 5 3 1 4 4 5 4 6 4 8 6 2 4 4 7 3 9 3 3 6 7 4 5 5
## [817] 4 2 5 3 4 2 5 5 3 5 4 4 5 8 7 6 3 4 3 2 2 4 7 6
## [841] 4 4 4 3 6 4 5 1 6 6 4 6 4 7 5 7 5 4 9 7 9 5 3 8
## [865] 6 5 5 4 5 8 4 8 3 2 2 5 11 8 6 10 3 5 5 9 3 11 5 3
## [889] 4 2 2 4 2 6 10 6 6 8 6 6 6 5 6 5 5 4 2 8 7 8 5 5
## [913] 4 6 4 5 4 3 6 4 4 7 9 7 3 3 4 4 1 4 5 8 3 3 1 6
## [937] 6 8 4 3 2 7 5 5 6 6 3 2 12 1 7 7 5 8 4 3 5 4 2 3
## [961] 4 5 6 3 5 5 8 4 7 7 8 2 6 8 6 4 5 5 3 11 5 2 3 2
## [985] 2 4 9 10 4 3 5 5 7 3 6 3 4 4 2 6 2 3 4 1 7 8 7 6
## [1009] 5 4 7 3 6 1 3 1 3 6 8 4 7 6 8 5 3 4 4 8 3 4 3 6
## [1033] 1 6 4 5 4 5 4 8 6 5 7 1 1 7 5 11 10 7 3 6 7 5 6 6
## [1057] 6 6 4 2 3 6 10 9 7 5 2 8 8 8 6 6 3 6 5 10 8 4 3 4
## [1081] 4 5 11 2 3 4 7 2 3 7 6 5 7 2 4 4 5 4 4 9 8 4 5 12
## [1105] 6 9 3 5 6 7 7 4 8 3 5 5 3 4 3 10 4 11 5 9 2 4 5 2
## [1129] 4 8 5 4 2 6 9 10 4 9 3 6 5 6 9 6 10 6 4 5 8 6 5 2
## [1153] 6 9 4 4 4 6 1 4 3 4 6 6 9 9 3 8 4 5 6 2 4 4 7 9
## [1177] 1 5 2 6 3 3 3 7 7 6 7 6 4 9 7 4 3 5 6 6 3 9 1 4
## [1201] 4 5 1 12 3 7 4 3 6 3 6 7 4 1 5 5 12 5 10 3 6 7 7 2
## [1225] 5 3 6 2 8 1 7 3 5 6 2 9 4 3 5 5 6 7 4 3 10 3 5 3
## [1249] 9 1 5 1 5 7 5 4 5 5 3 7 5 5 4 2 6 7 4 2 5 6 5 8
## [1273] 7 5 6 9 4 9 5 5 10 7 4 3 6 4 2 3 12 7 5 3 7 8 5 6
## [1297] 7 6 5 3 7 6 6 4 2 5 5 8 6 1 11 7 4 3 3 8 4 9 4 3
## [1321] 7 3 5 7 8 2 5 5 5 4 8 7 8 5 5 3 9 4 4 7 6 6 4 6
## [1345] 5 4 2 1 3 6 3 0 5 7 2 5 1 1 9 3 3 3 7 5 3 7 5 2
## [1369] 7 7 3 3 7 4 6 10 2 5 5 6 3 6 9 7 6 6 5 6 4 1 9 4
## [1393] 6 2 5 3 4 6 6 3 3 6 7 5 3 3 9 4 5 8 4 3 3 4 6 6
## [1417] 9 3 4 2 4 8 6 5 6 2 3 6 6 3 3 2 7 7 4 5 9 4 5 5
## [1441] 4 7 5 3 6 6 2 5 4 5 8 6 6 5 4 3 3 4 6 5 4 5 6 2
## [1465] 4 2 1 5 5 4 6 4 1 2 5 8 8 1 6 6 5 5 8 5 5 3 3 6
## [1489] 3 3 4 8 3 6 2 4 6 10 5 6 6 3 5 6 8 6 4 4 6 6 2 7
## [1513] 6 3 5 7 3 3 4 6 9 5 6 3 8 6 4 5 4 9 2 4 8 4 7 3
## [1537] 8 8 10 3 4 3 9 7 5 10 7 5 6 9 9 3 2 7 2 4 7 3 4 5
## [1561] 4 2 3 5 3 5 5 4 3 5 9 9 4 8 5 6 4 3 7 0 4 3 3 5
## [1585] 5 8 9 5 5 4 5 6 5 6 7 6 9 3 8 8 6 7 3 4 3 6 4 4
## [1609] 2 1 3 2 7 3 8 7 6 5 2 1 5 6 4 4 1 1 8 7 4 4 6 0
## [1633] 8 3 5 4 5 7 4 9 7 11 10 5 5 6 4 2 7 5 3 6 5 3 5 3
## [1657] 11 6 6 3 1 5 6 8 5 4 3 5 6 5 6 3 4 6 6 4 5 3 6 3
## [1681] 2 0 6 4 4 5 7 7 8 5 5 4 4 3 8 4 2 4 3 6 4 6 4 6
## [1705] 10 6 5 6 2 5 5 3 5 5 4 4 4 3 4 6 5 0 6 3 0 5 1 6
## [1729] 4 4 9 7 6 5 8 5 3 6 2 3 4 7 6 3 8 5 6 3 7 5 3 4
## [1753] 4 1 2 5 5 5 1 5 2 8 6 5 2 4 6 5 7 3 3 1 5 3 4 2
## [1777] 4 4 6 3 8 6 7 4 9 7 5 7 5 4 5 3 5 11 6 4 7 3 6 7
## [1801] 5 3 4 5 4 9 7 2 1 3 5 11 1 8 5 7 6 9 1 4 4 6 4 4
## [1825] 8 2 8 3 4 12 5 6 2 5 9 6 6 1 4 5 7 2 6 7 6 7 5 4
## [1849] 5 2 2 1 2 6 11 6 6 7 6 4 5 6 3 3 2 5 4 2 12 5 7 9
## [1873] 2 4 4 5 2 6 4 1 7 5 11 4 7 6 5 5 3 3 3 6 7 5 5 7
## [1897] 7 9 5 3 9 4 8 4 6 4 6 5 10 4 5 4 3 4 3 6 5 8 3 4
## [1921] 11 7 3 4 5 4 4 7 9 1 7 6 5 5 4 5 3 5 3 3 5 7 2 5
## [1945] 4 3 3 6 4 5 7 5 2 3 4 3 5 6 7 4 4 4 7 4 6 3 8 4
## [1969] 5 4 2 2 4 4 1 6 8 3 4 7 6 3 5 6 8 3 5 4 5 8 4 2
## [1993] 4 4 4 8 6 5 5 9 3 6 8 6 7 3 2 11 2 7 6 7 9 3 6 5
## [2017] 4 3 8 10 4 7 5 2 4 11 6 6 4 4 8 3 6 6 4 11 6 3 5 5
## [2041] 4 7 3 4 2 3 7 8 7 4 9 3 6 3 4 3 6 2 5 3 4 7 6 9
## [2065] 7 5 6 3 5 3 6 4 5 4 4 2 7 7 5 10 8 4 2 7 1 6 8 9
## [2089] 7 1 6 7 8 12 4 3 5 4 2 6 6 7 6 7 4 6 3 6 7 5 11 4
## [2113] 5 4 7 4 3 9 3 4 5 1 4 2 2 1 2 3 8 5 1 1 3 9 3 9
## [2137] 5 9 1 3 6 3 3 7 7 2 3 8 6 4 4 8 7 3 9 1 3 5 5 6
## [2161] 5 3 2 7 9 8 5 9 4 3 6 6 6 3 6 10 8 12 10 7 3 6 6 2
## [2185] 1 4 4 5 3 4 6 3 5 5 3 6 4 5 2 6 4 8 3 5 6 5 6 4
## [2209] 6 5 8 3 6 4 5 5 2 5 5 7 6 9 1 6 6 3 5 6 3 6 5 4
## [2233] 5 4 4 4 7 4 6 5 3 0 12 6 6 5 5 3 2 4 6 8 7 8 4 6
## [2257] 2 6 3 4 3 2 3 7 4 1 5 7 6 6 9 4 4 4 3 4 3 8 2 11
## [2281] 7 2 2 8 3 6 5 5 2 6 6 7 3 0 6 2 7 3 6 4 6 9 2 5
## [2305] 2 5 3 5 8 3 2 6 8 5 13 5 1 8 7 4 5 1 3 4 8 6 1 1
## [2329] 6 4 10 5 2 3 8 3 3 7 4 6 7 5 5 3 5 4 3 5 3 4 4 5
## [2353] 5 6 4 5 8 8 9 6 5 8 7 5 5 7 6 1 1 4 1 4 4 7 4 2
## [2377] 6 8 4 5 6 4 1 5 3 7 5 4 10 5 6 5 4 4 3 6 5 4 8 7
## [2401] 4 4 6 4 8 8 2 5 6 5 2 6 9 2 3 13 5 5 4 5 5 4 9 5
## [2425] 6 4 8 7 3 6 4 2 6 5 7 7 3 5 5 5 3 4 7 3 7 4 3 3
## [2449] 3 1 4 6 5 5 5 4 3 5 5 5 6 2 2 5 2 3 3 3 6 5 6 6
## [2473] 5 4 6 0 4 6 1 9 3 7 6 4 4 1 3 7 5 4 6 7 5 5 6 2
## [2497] 3 5 6 6 4 3 2 5 7 4 9 7 6 7 7 8 4 9 2 4 7 4 3 3
## [2521] 4 4 6 3 7 3 5 8 4 5 7 12 9 3 7 3 3 3 7 2 3 5 8 4
## [2545] 2 4 2 1 3 4 4 7 4 4 4 3 9 6 5 7 4 3 6 7 11 3 7 6
## [2569] 5 6 6 5 2 1 1 3 3 5 3 3 5 5 6 2 5 6 6 7 4 3 4 5
## [2593] 3 3 3 3 7 3 4 6 5 6 10 5 11 3 0 3 3 8 4 2 6 4 4 7
## [2617] 2 9 3 2 4 9 1 5 1 4 5 3 7 3 6 7 4 7 3 8 8 7 4 6
## [2641] 3 4 4 4 6 5 4 6 8 7 3 6 2 6 10 4 5 6 5 8 12 3 4 5
## [2665] 1 6 7 4 8 2 3 5 1 8 4 9 5 8 0 2 5 6 4 3 1 7 5 2
## [2689] 4 5 1 6 5 6 4 5 4 8 9 4 4 6 5 5 4 3 4 2 6 2 3 5
## [2713] 6 1 7 3 9 4 4 4 4 5 2 7 2 7 2 3 10 3 4 3 3 4 9 5
## [2737] 9 9 3 4 6 9 7 11 3 4 4 7 7 3 6 3 7 4 7 6 6 3 3 2
## [2761] 4 4 4 5 3 8 7 9 6 7 2 4 4 5 9 8 4 5 2 1 8 6 6 3
## [2785] 3 8 2 5 6 4 3 3 3 4 8 9 6 8 5 6 2 9 9 7 0 8 2 9
## [2809] 5 2 2 5 5 4 4 3 4 7 2 3 6 10 1 9 10 6 4 4 4 1 4 2
## [2833] 6 9 4 3 6 3 4 11 5 0 4 9 2 2 3 6 6 6 5 5 6 6 3 8
## [2857] 2 6 6 4 6 6 9 6 3 2 2 2 7 2 4 10 6 5 2 5 11 5 3 5
## [2881] 4 3 5 8 4 4 4 10 2 4 2 10 5 1 2 5 2 7 7 8 7 2 6 2
## [2905] 3 3 5 9 4 6 3 5 5 6 8 7 10 6 1 6 5 3 4 2 6 6 7 4
## [2929] 7 4 4 3 7 3 5 5 8 5 8 6 6 11 3 6 8 4 1 7 1 4 9 3
## [2953] 7 7 4 10 5 3 4 3 7 6 4 13 4 5 4 3 7 5 3 4 10 3 3 9
## [2977] 6 4 3 2 2 3 7 5 1 4 7 8 6 4 5 6 2 10 6 6 4 2 2 5
## [3001] 4 4 8 5 6 2 3 5 4 5 4 4 6 7 3 5 2 5 3 6 4 4 5 5
## [3025] 4 5 5 6 5 10 6 4 7 8 4 6 3 3 4 7 4 5 5 5 5 9 3 6
## [3049] 4 4 7 4 4 4 5 4 11 4 2 2 5 3 5 5 6 6 8 5 14 9 8 6
## [3073] 0 2 6 4 4 0 2 4 4 2 7 4 6 3 3 2 9 8 4 5 3 9 5 3
## [3097] 3 1 6 8 4 2 7 5 7 5 6 3 7 8 3 3 3 3 5 4 5 6 5 3
## [3121] 4 6 9 5 3 2 9 8 3 3 5 5 6 3 3 4 4 5 4 5 7 4 5 7
## [3145] 4 3 6 5 5 4 5 5 3 6 2 7 9 6 5 9 6 8 4 3 6 1 6 5
## [3169] 4 4 2 7 3 2 8 2 1 2 8 4 7 3 8 6 1 7 9 8 8 8 6 6
## [3193] 7 5 8 3 3 5 4 4 7 3 9 2 1 6 5 5 6 6 5 5 5 4 2 2
## [3217] 5 1 2 3 8 7 4 3 5 7 2 8 7 5 10 6 7 6 4 7 4 8 4 3
## [3241] 8 8 5 6 7 6 8 5 7 3 1 5 3 7 3 3 3 2 8 2 5 6 6 4
## [3265] 4 3 6 6 5 3 0 5 6 3 5 5 4 6 8 4 11 6 8 1 5 3 8 2
## [3289] 5 6 4 6 5 7 6 3 4 5 6 4 5 4 7 5 2 4 6 2 3 2 2 7
## [3313] 3 5 6 4 5 6 9 7 4 6 6 5 5 8 7 6 2 2 4 6 6 4 7 5
## [3337] 4 6 3 2 6 3 7 5 9 7 3 4 5 1 5 3 5 5 6 2 9 3 2 3
## [3361] 5 8 5 3 4 3 5 7 4 6 5 5 4 3 1 4 4 1 5 6 3 5 3 5
## [3385] 5 6 8 6 6 5 7 4 5 8 3 7 7 6 7 3 3 7 3 4 4 4 5 2
## [3409] 10 4 2 3 5 6 1 4 11 9 2 7 5 4 4 3 8 6 6 12 7 5 3 10
## [3433] 6 6 6 8 5 6 9 6 5 8 6 3 7 5 6 4 3 5 5 9 5 2 1 3
## [3457] 6 8 2 5 7 6 6 5 7 3 5 5 5 4 5 5 3 6 6 6 6 6 11 5
## [3481] 8 5 1 6 6 5 10 2 6 5 9 7 5 4 6 6 8 12 9 5 5 5 6 4
## [3505] 6 4 6 9 5 3 10 8 3 1 4 4 2 6 4 1 10 2 7 6 0 2 2 4
## [3529] 5 4 3 3 7 5 5 4 7 2 1 4 1 3 5 3 4 12 4 3 7 4 7 5
## [3553] 2 8 7 6 0 4 5 6 3 1 7 2 3 3 5 4 4 4 5 7 7 3 5 9
## [3577] 5 4 5 6 1 4 6 3 5 7 6 7 6 4 6 4 4 6 3 6 5 3 7 8
## [3601] 3 6 10 10 6 5 1 6 4 6 5 7 6 6 5 3 9 4 8 2 4 3 5 7
## [3625] 5 8 4 6 1 4 6 5 6 6 5 4 10 2 8 5 4 6 9 4 3 6 8 5
## [3649] 2 8 10 6 4 5 6 6 7 4 4 2 7 4 4 5 2 8 6 6 5 2 6 5
## [3673] 5 3 9 3 7 3 4 3 6 5 8 5 3 4 8 8 6 6 8 4 6 5 7 3
## [3697] 5 2 6 4 3 1 4 4 10 0 1 1 0 4 3 8 6 6 9 2 3 6 5 6
## [3721] 3 7 4 4 4 5 6 3 4 5 5 7 5 8 9 10 7 8 5 5 9 3 3 3
## [3745] 7 4 12 5 5 5 3 7 6 8 2 7 3 3 4 4 5 5 9 10 8 4 3 2
## [3769] 3 5 0 5 5 4 4 5 2 8 5 1 1 5 5 5 8 3 4 1 2 5 5 6
## [3793] 9 3 8 2 10 7 4 1 1 5 5 6 5 6 8 8 6 2 6 7 4 5 6 2
## [3817] 5 5 8 6 6 6 5 6 3 0 6 5 8 4 6 7 7 3 6 6 4 11 2 10
## [3841] 3 4 5 5 3 6 11 3 7 5 3 5 3 6 8 5 2 11 4 3 3 2 6 7
## [3865] 4 4 0 3 9 4 1 6 2 4 4 5 10 2 4 3 3 8 7 9 5 3 6 4
## [3889] 2 15 4 8 4 4 5 6 4 5 7 4 5 3 4 3 8 5 4 11 7 8 2 3
## [3913] 5 4 5 6 3 9 6 6 1 5 3 8 7 4 7 3 4 3 4 3 7 5 6 11
## [3937] 3 5 6 4 8 9 2 4 6 9 5 7 6 5 3 4 4 2 2 2 9 8 2 7
## [3961] 3 5 5 4 6 5 6 6 6 4 4 7 7 14 8 7 4 6 5 3 7 6 4 2
## [3985] 5 5 4 7 10 5 5 3 7 8 3 4 4 3 1 8 5 4 2 4 5 6 7 7
## [4009] 4 10 6 4 6 7 6 7 7 5 6 5 6 3 5 6 6 4 4 5 5 4 3 6
## [4033] 2 4 5 5 2 4 8 7 5 6 4 6 4 6 4 5 9 8 7 6 1 3 8 9
## [4057] 6 8 9 2 7 5 3 2 7 5 3 3 7 9 2 3 10 3 3 4 5 5 7 5
## [4081] 1 5 4 4 5 7 7 6 8 3 4 4 4 3 7 7 8 3 5 9 6 2 4 6
## [4105] 3 6 3 6 3 3 4 4 3 4 7 6 4 5 4 7 8 3 6 7 6 7 4 3
## [4129] 5 7 3 7 5 6 6 6 9 7 7 6 6 4 13 4 4 6 6 7 5 3 6 6
## [4153] 4 4 4 6 3 2 5 6 10 3 6 5 5 5 3 10 1 5 6 6 7 8 3 2
## [4177] 12 4 3 4 6 6 6 3 3 5 7 8 4 2 4 6 9 6 10 1 3 3 6 5
## [4201] 6 8 4 6 3 7 5 4 2 3 10 5 8 7 6 3 5 4 8 6 2 8 4 6
## [4225] 5 4 5 7 11 3 3 4 6 1 6 6 5 4 7 5 3 6 4 5 5 4 9 4
## [4249] 4 7 2 4 10 2 4 4 7 4 2 8 3 1 5 3 8 6 6 7 4 2 4 7
## [4273] 8 4 5 3 6 3 4 9 4 7 2 5 6 4 4 8 4 4 5 3 9 5 4 4
## [4297] 5 4 3 2 4 10 4 9 4 4 3 10 5 5 4 2 2 2 6 5 3 4 7 4
## [4321] 10 6 2 2 6 6 7 3 8 3 5 3 6 5 1 6 9 6 2 5 6 2 5 4
## [4345] 8 2 8 6 6 1 5 4 1 1 3 5 6 7 4 8 7 7 5 4 3 4 3 6
## [4369] 8 7 7 6 2 5 8 2 7 4 6 6 3 8 8 5 9 6 6 9 6 3 5 9
## [4393] 9 1 10 8 9 11 6 4 10 5 5 7 6 7 3 4 6 5 8 7 3 2 2 3
## [4417] 1 6 9 3 4 8 7 3 6 6 3 3 4 7 3 6 9 2 4 6 7 3 7 4
## [4441] 6 2 2 5 2 5 2 6 5 4 2 1 6 5 4 6 4 3 6 7 6 7 4 1
## [4465] 2 4 3 8 2 6 6 4 5 6 7 5 6 3 7 4 5 4 4 7 4 3 5 3
## [4489] 4 10 7 5 2 3 4 8 4 3 10 7 3 3 3 6 3 5 5 5 5 6 5 7
## [4513] 5 5 2 5 5 7 4 4 2 5 1 3 4 2 3 8 7 2 6 1 5 7 8 8
## [4537] 7 4 5 3 5 5 3 6 2 7 4 4 4 1 1 2 5 2 5 2 3 4 9 5
## [4561] 5 2 5 7 3 6 4 4 5 2 4 5 5 3 6 8 3 4 3 5 4 3 2 6
## [4585] 7 3 6 5 0 6 3 6 5 5 3 5 7 3 10 2 2 5 2 3 5 6 4 5
## [4609] 5 4 10 4 6 6 5 5 4 4 5 1 2 6 6 7 8 5 4 9 7 2 10 5
## [4633] 3 6 1 7 1 10 7 4 8 6 5 6 3 6 2 3 5 8 2 3 3 5 4 6
## [4657] 6 9 6 3 4 7 5 8 5 7 4 6 5 6 3 6 3 2 6 4 0 2 5 5
## [4681] 6 7 3 4 4 3 5 5 6 2 5 9 4 4 5 6 8 5 1 5 7 5 5 6
## [4705] 6 6 5 7 5 16 4 5 5 3 6 2 5 4 6 5 10 4 6 4 6 3 7 8
## [4729] 6 4 2 5 1 8 4 3 4 5 1 6 3 4 2 7 7 5 3 3 9 7 6 5
## [4753] 1 3 3 5 3 9 5 6 3 5 9 2 5 5 9 3 3 2 3 3 3 8 2 2
## [4777] 8 8 5 5 6 4 1 4 4 2 7 11 6 4 6 5 3 10 2 10 5 5 2 6
## [4801] 2 5 9 4 6 4 5 7 4 6 6 6 1 4 4 7 7 6 4 6 3 10 8 4
## [4825] 6 5 4 2 7 8 2 6 8 4 3 9 1 6 4 5 7 4 12 7 1 3 3 4
## [4849] 8 5 3 3 8 6 9 6 6 11 7 3 7 5 3 7 5 5 6 2 2 7 7 5
## [4873] 5 5 5 2 2 3 4 4 2 2 5 7 5 6 4 6 3 4 3 4 6 6 7 8
## [4897] 6 6 3 7 5 4 8 2 5 6 4 8 6 1 2 8 6 8 6 3 1 4 4 5
## [4921] 4 6 7 8 2 6 5 6 10 6 3 2 3 5 4 4 5 3 8 5 3 8 5 6
## [4945] 3 6 5 3 4 9 8 5 3 6 3 7 4 3 5 3 1 8 6 1 6 5 4 8
## [4969] 3 5 5 6 7 5 4 7 3 6 1 7 10 7 3 5 5 3 3 2 9 6 7 14
## [4993] 2 3 5 5 5 4 4 5# Gráfico de barras
barplot(table(llegadas),col=12,main="Llegadas de solicitudes por hora",xlab="Numero de solicitudes",ylab="Frecuencia")
# Probabilidad empírica de menos de 3 solicitudes
prob_menos3 <- mean(llegadas < 3)
prob_menos3## [1] 0.1194Interpretación:
La mayor parte de las horas registra entre 3 y 7 solicitudes, lo que
muestra que el promedio se aproxima a 5. La probabilidad empírica de que
en una hora se presenten menos de 3 solicitudes es
0.1194, lo que evidencia que este evento es poco
frecuente.
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.
# Distribución Exponencial con media = 12
tiempos <- rexp(5000, rate = 1/12)
tiempos## [1] 9.559767e+00 2.913276e+01 2.493287e+00 7.455807e+00 1.217063e+01
## [6] 2.012806e+00 1.249677e+01 1.419500e+01 2.981612e+01 7.882683e+00
## [11] 7.251096e+00 2.284153e+01 8.383992e+00 1.219748e+00 5.904560e+00
## [16] 9.545784e+00 3.912352e+01 1.170554e+01 4.430726e+00 2.958277e+00
## [21] 7.612759e+00 7.395137e-02 1.134416e+01 6.276973e+00 1.802634e+01
## [26] 1.087066e+01 2.059830e+01 5.384855e+00 1.993985e+01 2.670053e+00
## [31] 4.135381e+00 3.717360e+01 1.506044e+00 1.115666e+00 1.266335e+00
## [36] 9.487375e+00 8.226514e+00 1.307743e+01 5.991655e+00 1.458441e+01
## [41] 3.423895e+01 3.293056e+00 3.733149e+00 2.304724e+00 4.926332e+00
## [46] 1.450961e+01 1.382720e+01 1.113431e+01 7.102068e+00 1.318610e+01
## [51] 3.066163e+01 3.180007e+01 2.046128e-01 7.249435e+00 2.202678e+01
## [56] 2.420624e+01 2.980493e+00 2.169861e+00 1.824686e+01 2.358853e+01
## [61] 1.167559e+01 4.883731e+00 4.717269e+00 4.304276e+00 1.928957e+01
## [66] 7.782018e+00 4.363646e+00 1.652009e+01 2.146281e+01 6.733845e+00
## [71] 1.752274e-01 2.647797e+00 2.580066e+01 6.047543e+01 4.180703e+00
## [76] 1.363443e+00 1.194902e+01 9.102858e+00 2.381824e+00 2.401140e+01
## [81] 2.737714e+01 9.733502e+00 1.005375e+01 1.292797e+01 4.825683e+01
## [86] 1.324942e+01 1.113902e+01 4.458036e+00 1.322993e+01 5.300434e+00
## [91] 1.168366e+01 1.315006e+01 9.787536e+00 2.712009e+00 1.073374e+01
## [96] 1.160373e+01 1.312147e+01 2.880994e+01 5.278084e+01 7.659314e+00
## [101] 3.567145e+00 3.478301e+00 8.983963e+00 3.065608e+00 6.988973e+00
## [106] 1.482596e+01 2.194140e+01 1.369852e+01 2.080553e+00 1.659392e+00
## [111] 2.101080e+01 5.404076e+00 1.190672e+01 1.262155e+01 2.055091e+01
## [116] 2.086191e+01 1.099803e+01 4.563168e+00 3.878544e+00 1.757597e+01
## [121] 1.969053e+00 2.411428e+01 1.293953e+00 3.400682e+00 4.446163e+00
## [126] 3.016691e+01 3.980281e+01 2.338389e+00 5.803815e+01 2.835579e+00
## [131] 2.356091e+01 4.875280e+00 3.353122e+01 1.838222e+01 4.425064e+01
## [136] 5.917429e+00 1.193072e-01 4.938463e+00 4.864691e+00 4.060758e+01
## [141] 2.268896e+01 1.015687e+01 2.316772e+00 6.796426e+01 1.842027e+00
## [146] 2.108799e+01 9.584047e+00 9.795203e+00 8.923105e+00 5.958076e+00
## [151] 2.932096e+01 2.427487e+01 3.210546e+01 3.858490e+00 1.018145e+01
## [156] 3.607840e+00 3.929465e+00 3.111823e+00 8.671528e+00 1.484244e+00
## [161] 3.588894e+01 1.084993e+01 6.250867e-01 8.482759e+00 4.696110e+01
## [166] 1.771759e+01 1.066754e+01 1.307852e+01 1.086245e+01 6.685236e+00
## [171] 1.000616e+01 1.393909e+01 4.357572e+00 2.301748e+00 6.272496e-01
## [176] 9.984896e+00 1.272083e+01 3.179381e-01 2.573481e+01 2.074616e+01
## [181] 8.289258e+00 1.682512e-01 1.759857e+01 1.836340e+00 7.884807e+00
## [186] 6.483877e+01 3.674163e+00 1.392817e+01 1.246996e+01 2.566980e+00
## [191] 8.724407e+00 3.719945e+01 1.429271e+01 1.291674e+01 1.253529e+01
## [196] 2.911250e+01 1.862492e+00 1.349320e+01 2.781772e+00 7.050611e+00
## [201] 6.589317e+00 5.575087e+00 5.661390e-01 1.495691e+01 1.885843e-01
## [206] 5.095269e+00 6.608192e+00 4.368255e+00 1.752568e+01 2.242564e+00
## [211] 9.620981e+00 1.309513e-01 2.742282e+01 1.216118e+01 1.641159e+01
## [216] 1.869967e+00 2.217558e+01 1.683562e+01 3.804549e+00 1.871547e+01
## [221] 3.605988e+00 1.112622e+01 3.351144e+00 1.264764e+01 4.901892e+00
## [226] 1.096851e+01 3.180992e+00 1.519251e+01 2.349794e+00 3.617974e+00
## [231] 4.531608e+00 1.614122e+01 5.735986e+01 2.631214e+00 1.969929e+00
## [236] 2.520384e+00 3.781749e+00 1.955545e+00 9.832505e+00 1.534182e+01
## [241] 3.154218e+00 6.480888e+00 1.815594e+01 2.174894e+01 3.832662e+00
## [246] 5.149175e+00 3.496149e+00 1.830225e+00 7.777336e+00 4.518864e+00
## [251] 8.323485e+00 4.933989e+00 1.583768e+01 5.698466e+00 5.492637e+01
## [256] 3.468951e+00 2.161278e+01 2.102682e+00 1.232532e+00 4.553790e+01
## [261] 2.569038e+01 1.676298e+01 8.008533e+00 1.005755e+01 1.209009e+01
## [266] 2.126317e+00 5.459623e+00 6.738000e+00 1.924230e+01 2.403870e+01
## [271] 2.518830e+00 1.097315e+00 1.169138e+01 9.747067e+00 1.705364e+00
## [276] 2.264708e+01 7.343932e+00 1.376610e+01 5.990580e-01 1.614177e+00
## [281] 6.685899e+00 7.125669e-01 4.733833e+00 7.797472e-03 1.557579e+01
## [286] 2.580501e+01 3.394481e+00 6.974269e+00 3.326991e+01 3.634014e+00
## [291] 8.790371e+00 6.327719e-01 6.950430e+00 1.304874e+01 2.075076e+01
## [296] 5.067148e+00 2.343269e+01 2.438019e+01 7.861720e+00 3.389051e+01
## [301] 9.134510e+00 5.963518e+00 2.135103e+00 2.954619e+01 3.749348e+01
## [306] 3.609515e+00 9.163899e+00 6.425792e+01 1.322754e+01 1.285834e+00
## [311] 2.079190e+00 1.205394e+01 7.920020e-01 3.820269e+01 1.773618e+01
## [316] 4.269095e+00 2.582267e+00 6.550117e+00 2.804489e-01 2.486460e+01
## [321] 6.462809e+00 1.072216e+01 1.660812e+00 5.022782e+01 2.853456e+01
## [326] 3.406284e+00 1.394245e+00 5.002172e+00 7.011266e+00 8.820270e+00
## [331] 2.855195e+01 1.161606e+01 1.173463e+01 1.957599e+01 6.472623e+00
## [336] 1.838553e+01 4.102541e+00 3.963020e+00 7.363466e+00 1.292549e+01
## [341] 1.245757e+01 6.435820e+00 2.322118e+01 8.462098e+00 6.992967e-01
## [346] 1.670508e+01 5.480239e+00 1.528305e+00 1.257281e+01 2.212941e+01
## [351] 1.584051e+00 9.801687e+00 9.152647e+00 1.048615e+01 1.433750e+00
## [356] 7.335441e+01 2.275188e+00 1.949646e+01 2.409212e+00 2.565542e+00
## [361] 1.134693e+01 2.901081e+00 1.441615e+01 6.129188e+00 3.254646e+01
## [366] 1.104121e+01 1.844107e+01 8.118961e+00 2.360356e+00 4.972591e+00
## [371] 8.118262e+00 2.102471e+01 1.281378e+01 1.598508e+01 2.359619e+01
## [376] 1.152634e+01 1.535812e+01 5.042742e+00 1.306196e+00 1.088094e+00
## [381] 1.448979e+01 5.312395e+00 4.010637e+00 2.875345e+00 6.354826e+00
## [386] 6.971211e+00 5.006763e+00 9.040308e+00 7.667751e+00 1.017046e+01
## [391] 5.223365e-01 1.683981e+00 3.388277e+00 9.365765e+00 1.056011e+00
## [396] 9.701494e+00 2.971003e+00 1.314191e+01 1.965887e+01 5.576590e+01
## [401] 1.955119e+01 4.880285e+00 1.322011e+01 8.088093e-01 4.715224e+00
## [406] 1.688533e+01 6.578255e+00 4.410057e+01 8.965199e+00 9.215088e+00
## [411] 8.309669e+00 3.092475e+01 3.833155e+01 3.318104e+00 7.939195e-01
## [416] 1.555509e+01 4.260426e+00 2.565492e+00 1.513047e+01 2.535877e+01
## [421] 1.283480e+01 7.980483e+00 1.734659e+01 8.527318e+00 2.207502e+00
## [426] 9.829024e+00 1.528479e+00 2.024758e+01 2.045820e+01 8.256128e+00
## [431] 1.536883e+00 2.950747e+01 1.161005e+01 3.859928e+01 1.491006e+00
## [436] 5.594497e+00 1.313883e+00 4.946532e+00 4.344976e+01 9.452732e-01
## [441] 1.374871e+01 7.311063e+00 2.109016e+01 3.466063e+01 5.527824e+00
## [446] 1.028182e+01 1.363076e+01 7.295926e+00 1.692550e+01 2.089595e+01
## [451] 6.186683e+00 9.902525e+00 5.266014e-01 7.508858e+00 8.236168e+00
## [456] 3.224480e+00 9.818794e+00 8.046809e+00 9.431808e+00 1.573825e+01
## [461] 2.690847e+01 2.874867e+00 7.060873e+00 1.199329e+00 3.001399e+01
## [466] 1.725784e+01 2.393167e+01 1.739256e+01 3.502824e+01 3.110800e+00
## [471] 3.368846e+01 7.345252e-01 2.211192e+00 5.653260e-01 1.715980e+01
## [476] 3.613815e+01 7.490598e+00 2.543146e+01 2.179186e+00 1.201351e+01
## [481] 3.210469e+01 2.309770e+01 2.230381e+00 1.375869e+01 8.074271e+00
## [486] 4.789463e+00 1.401552e+01 1.720286e+01 3.764733e+00 1.428479e+01
## [491] 6.040638e-01 1.806200e+01 2.224337e+01 1.892734e+00 5.047138e+00
## [496] 5.360415e-01 5.962661e+00 6.611187e+00 7.477279e+00 2.453454e+01
## [501] 1.566524e+00 1.227166e+01 1.373945e+01 1.301926e+01 1.442575e+01
## [506] 1.039115e+01 9.553557e-01 2.335324e+01 1.190856e+01 2.058736e+01
## [511] 1.001882e+01 5.120602e+00 1.841503e+01 3.471524e+00 1.536897e+00
## [516] 1.057200e+01 4.192086e+00 1.499535e+00 4.927626e+00 1.275227e+01
## [521] 7.514975e+00 2.412587e+01 4.531680e+01 5.380915e+00 4.436180e+00
## [526] 1.412903e+00 1.089740e+01 1.842922e+00 1.984313e+00 1.042286e+01
## [531] 5.443627e+00 1.785088e+01 7.620648e+00 3.213077e+00 2.922691e+01
## [536] 2.035650e+01 2.400459e+01 5.652716e+01 9.107011e+00 1.051528e+00
## [541] 2.513854e+01 1.759469e+01 1.186623e+01 6.551908e+00 4.565396e-01
## [546] 1.013171e+01 1.334047e+01 1.858475e+00 1.013517e+01 4.437988e+00
## [551] 5.945654e+00 9.148431e+00 1.853105e+01 2.692856e+01 1.554152e+01
## [556] 1.333066e+00 2.116366e+01 4.205603e+00 6.758756e+00 2.423027e+00
## [561] 7.156685e+00 3.767302e+01 2.507255e+01 2.302842e+01 1.877663e+01
## [566] 7.642955e+00 4.830814e+00 2.773814e+01 1.626201e+01 6.758234e+00
## [571] 1.413247e+01 2.170160e+01 1.039241e+01 9.176782e+00 4.361352e+00
## [576] 1.462510e+01 1.862699e+01 9.234432e+00 8.871878e+00 4.844541e+00
## [581] 9.123007e+00 1.687487e+00 2.380178e+01 2.708036e+01 1.449887e+00
## [586] 6.549112e+00 2.201938e+01 5.814050e+00 1.579093e+01 1.421221e+00
## [591] 1.517438e+00 4.103026e+01 1.060483e+01 1.895649e+01 1.719443e+01
## [596] 8.384050e-01 4.270231e+01 7.773401e+00 1.997909e+01 2.692036e+01
## [601] 2.066336e+01 5.096659e+00 3.333560e+00 4.301144e+01 2.814259e+01
## [606] 3.336144e+00 2.564858e+01 8.610044e-01 2.635442e+01 1.739526e+01
## [611] 1.430410e+01 8.356148e-01 1.705240e+00 5.504511e+00 8.660004e-01
## [616] 1.094917e+01 1.547914e+01 1.892571e+01 3.051549e+01 1.256292e+00
## [621] 9.640347e+00 2.525670e-01 1.206144e+00 2.071393e+00 2.620957e+00
## [626] 2.993861e+00 3.402207e+00 8.564480e+00 4.141112e+00 4.379981e-01
## [631] 2.734470e+01 1.287898e+01 3.730844e+01 6.878763e+00 2.711753e+01
## [636] 1.092140e+01 1.095768e+01 3.334251e+01 3.163585e+01 3.835085e+00
## [641] 1.365614e+00 2.065965e+01 5.524421e+00 1.002939e+01 7.023530e+00
## [646] 9.546228e+00 3.033143e+00 7.103482e+00 6.177771e+00 1.678163e+01
## [651] 7.689539e-02 3.235489e+00 8.144615e+00 1.897370e+01 6.696007e+00
## [656] 1.922192e+01 1.682568e+01 9.602829e-01 4.230802e+00 1.979788e+01
## [661] 2.462417e+01 2.578241e+00 1.152883e+01 4.929747e+00 5.797232e+00
## [666] 2.555924e+00 1.455962e+01 2.764551e+00 1.769313e+01 5.502887e+00
## [671] 2.619581e+01 9.731877e+00 6.500611e+00 3.304809e+00 5.912162e+00
## [676] 2.310970e+00 4.786493e+00 5.470171e+00 1.975337e+01 3.034120e+00
## [681] 5.269375e-01 1.269948e+00 2.121331e+00 2.252852e+01 1.158547e+00
## [686] 1.742298e+01 1.391019e+01 1.317202e+01 6.873276e+00 8.662845e+00
## [691] 2.715627e+00 1.367616e+01 1.108661e+01 1.513310e+00 1.731766e+01
## [696] 1.222944e+00 7.943077e-01 6.521445e+00 6.381328e+00 1.740743e+00
## [701] 4.718460e+00 5.609213e-01 1.475502e+01 1.735334e+01 4.209068e+01
## [706] 1.838393e+00 8.045302e-01 7.150321e+00 9.405062e+00 9.076111e+00
## [711] 1.790780e+00 3.541299e-01 2.362630e+01 1.466439e+01 1.919661e+00
## [716] 8.485784e-01 8.046476e-02 2.622435e+00 1.516805e+01 1.180053e+01
## [721] 6.645686e+00 8.151304e+00 1.474771e+01 1.445908e+01 2.562133e+01
## [726] 3.282484e+01 9.397670e+00 1.406890e+01 7.341295e+00 2.427843e+00
## [731] 3.087929e+01 3.917547e+00 5.020733e+00 2.977547e-01 1.438523e+01
## [736] 1.696370e+00 5.175666e+01 3.044915e+01 4.438239e+00 5.651652e+00
## [741] 1.601965e+01 1.731721e+00 4.076067e+01 9.911606e+00 1.243729e+01
## [746] 1.068653e+01 1.374501e+01 2.169775e+01 3.908900e+00 3.631771e+00
## [751] 1.248368e+01 9.297887e-01 2.431469e+00 1.015775e+01 1.132642e+01
## [756] 8.243860e+00 3.053821e+00 1.550589e-01 1.460638e+01 4.589863e+00
## [761] 3.947012e+00 1.737169e+01 6.134635e+00 8.713784e+00 5.529237e+00
## [766] 5.732660e+00 2.898266e+00 3.352712e+01 5.364550e+00 1.147915e+00
## [771] 2.833507e+00 6.963021e+00 1.926800e+01 4.477282e-01 1.662323e+01
## [776] 2.225986e+01 9.411105e-01 7.895092e+00 2.211996e+01 2.023129e+01
## [781] 1.226583e+00 2.021581e+01 1.357965e+01 6.133521e+00 1.016593e+01
## [786] 2.667632e+01 1.589134e+01 3.771190e+01 1.666277e+00 1.322868e+00
## [791] 1.278025e+01 6.459270e+00 1.539746e+00 2.040139e-02 6.561274e-01
## [796] 3.369846e+00 9.578678e+00 2.637289e+00 2.172629e+01 7.030296e+00
## [801] 1.903852e+01 8.420585e+00 2.268777e+00 2.793616e+01 1.998220e+00
## [806] 1.196435e+01 4.855580e+00 3.589631e-01 1.280468e+01 1.201611e+01
## [811] 1.640804e+01 9.985558e+00 2.190038e+01 6.793600e+00 7.189985e+00
## [816] 2.560412e+01 4.081290e+00 5.219265e+00 9.457064e+00 6.306061e-01
## [821] 4.549255e+00 1.010457e+01 3.830579e+00 3.072648e+01 1.836908e+01
## [826] 2.192387e+00 2.879617e+00 9.469436e+00 3.961746e-01 1.309517e+01
## [831] 6.809468e+00 1.167529e+00 1.010800e+01 1.681027e+01 9.725343e+00
## [836] 2.764627e+00 8.169437e+00 8.959292e+00 4.130836e+00 7.431777e+00
## [841] 1.311461e-01 2.538093e+00 2.597666e+01 1.269487e+00 4.290193e+01
## [846] 7.323046e+00 2.304784e+01 3.334919e+01 3.500659e+01 5.235538e+00
## [851] 1.332765e+00 1.902660e+01 1.135690e+00 3.146047e+01 1.579545e+00
## [856] 1.106049e+01 3.852331e+01 3.243965e+00 3.079408e+01 2.109802e+00
## [861] 6.622637e+01 4.089811e+01 2.271243e+00 2.924213e+01 1.133306e+01
## [866] 2.084955e+00 2.120940e+01 9.130818e+00 3.816669e+00 1.291483e+00
## [871] 1.649718e+01 1.526609e+00 9.448054e+00 1.897365e+01 1.458028e+01
## [876] 1.642331e+01 3.145304e+00 2.178656e+00 9.645000e-01 1.595612e+00
## [881] 3.152876e+01 5.613357e+00 5.261160e+00 1.840178e+01 4.238489e-01
## [886] 3.582010e+00 6.157181e+00 2.411221e-01 2.502400e+01 3.079233e+01
## [891] 1.308322e+01 1.442733e+01 1.088785e+01 8.691459e-01 1.226209e+01
## [896] 2.248031e+00 1.020878e+01 1.887677e-02 1.482063e+00 1.585430e+00
## [901] 9.266139e+00 1.103763e+01 8.797830e+00 6.856779e+00 2.978736e+01
## [906] 2.116618e+01 1.234662e+01 1.572553e+01 3.114442e+01 7.555839e-01
## [911] 8.856247e+00 9.845600e+00 9.069462e+00 2.686388e+00 2.832797e+00
## [916] 4.189595e+00 2.271625e+00 9.014528e+00 1.272358e+01 4.364845e+01
## [921] 4.577701e+01 3.968591e+00 1.145656e+01 1.124677e+01 1.097806e+01
## [926] 1.490935e+01 3.768458e+01 4.241022e+00 2.060153e-01 4.169362e-01
## [931] 6.825031e+00 5.976425e+01 8.877068e+00 2.022482e+01 1.171440e+01
## [936] 3.506276e+00 9.600608e+01 5.170653e+00 5.947281e+00 1.251512e+00
## [941] 1.387718e+00 4.379650e+00 4.081986e+00 6.736783e+00 2.251875e+00
## [946] 4.879133e+00 3.402178e+00 7.997326e+00 4.040373e+00 1.366020e+01
## [951] 1.264841e+01 2.590283e-01 1.392529e+00 3.049533e+01 1.053519e+01
## [956] 4.913894e-01 1.236075e+01 2.838860e+01 3.654125e+01 4.105901e+00
## [961] 2.915585e+00 5.758410e+00 1.780274e+01 8.732292e-01 1.385251e-01
## [966] 1.377193e+01 8.047968e+00 4.968187e+01 3.709195e+01 2.917694e+01
## [971] 3.545378e+01 2.855008e+00 2.568383e+01 3.724696e+00 4.487676e+00
## [976] 1.050030e+01 4.479092e+01 3.948634e+00 4.796492e+00 2.734941e+00
## [981] 2.114438e+00 3.949097e+00 1.461231e+01 2.782724e+01 1.418868e+01
## [986] 4.634618e+00 1.526983e+01 1.821599e+01 1.254862e+01 2.857761e+00
## [991] 1.405885e+01 1.303667e+01 1.245911e+01 1.767843e-01 7.532698e+00
## [996] 1.861641e+00 3.574749e+00 1.587753e+01 5.833888e+00 2.710701e+01
## [1001] 1.575124e+01 2.915679e+00 2.435193e+00 9.950375e+00 4.755345e+00
## [1006] 2.097910e+01 8.061975e+00 3.113045e+01 4.069008e+00 7.158593e+00
## [1011] 3.005516e+01 2.035578e+00 1.314517e+01 1.111794e+01 8.769419e+00
## [1016] 6.802044e+00 5.083540e+01 9.621992e+00 1.839115e+01 2.562933e+01
## [1021] 3.286162e+00 1.432493e+01 5.726919e+00 1.471421e+01 2.047348e+00
## [1026] 1.138066e+01 1.512471e+00 9.026116e-01 8.742156e+00 3.618184e+00
## [1031] 2.124436e+00 1.107934e+01 6.827186e+00 1.940487e+01 1.248483e+01
## [1036] 1.061861e-01 4.149515e+00 1.928332e+01 2.404275e+01 6.789504e+00
## [1041] 3.247857e+00 1.701012e+00 4.535836e+00 2.351718e+01 1.043210e+01
## [1046] 1.396043e+00 6.401619e+00 1.042400e+01 9.947161e+00 1.543188e+01
## [1051] 3.383738e+01 1.788191e+01 6.354273e+00 9.276784e+00 1.292451e+01
## [1056] 3.188423e+00 3.289699e+00 4.127527e+01 3.675257e-03 2.789483e+01
## [1061] 3.274802e+00 6.664584e+00 2.148328e+00 6.855568e+00 1.697861e+01
## [1066] 3.633503e+00 4.395950e+01 1.757975e+01 3.393427e-01 2.425395e+01
## [1071] 4.508543e+00 4.328003e-01 1.508995e+01 2.406201e+01 3.424868e+01
## [1076] 3.757450e+00 1.227654e+00 6.573144e+00 2.353959e+01 2.654403e+00
## [1081] 7.299776e+00 8.547528e+00 1.456409e+01 1.702822e+01 9.735464e+00
## [1086] 1.293809e+01 4.866815e-01 1.064382e-02 3.833295e+00 4.524354e+00
## [1091] 2.432320e+01 8.652285e+00 2.723464e+01 2.332118e+00 4.761711e+00
## [1096] 8.732472e+00 1.085423e+01 9.926373e+00 2.880192e+00 2.055846e+00
## [1101] 6.380536e+00 2.050475e+01 6.814020e+00 1.488570e+01 1.810656e+01
## [1106] 1.170374e+01 9.603020e+00 6.200630e-01 1.010429e+01 2.060744e+00
## [1111] 1.582623e+01 9.240954e+00 2.654921e+00 4.635375e+00 2.102812e+00
## [1116] 1.102227e+01 1.858302e+01 7.111524e+00 2.655669e+01 1.128214e+01
## [1121] 8.567006e+00 8.235807e+00 4.021807e-01 5.762655e+00 2.338730e-01
## [1126] 2.828893e+00 1.104989e+01 5.813405e+01 2.099796e+01 2.134452e-01
## [1131] 1.231326e+01 1.836070e+01 1.990215e+00 6.738908e+00 4.932482e+00
## [1136] 1.016766e+01 1.090686e+01 2.444446e+01 2.448224e+01 7.036623e+00
## [1141] 1.302361e+01 3.566303e+00 4.332476e+00 2.491934e+01 7.212834e-01
## [1146] 4.192034e+00 1.790565e+01 2.069989e+01 2.512783e+01 2.163433e+01
## [1151] 5.588545e+00 4.374190e+01 4.974437e+01 1.778323e+01 7.289361e+00
## [1156] 2.135209e+01 3.007798e+00 2.309228e+00 2.941647e+01 4.718567e+00
## [1161] 1.255588e+01 2.663314e+00 1.436755e+01 6.266388e+01 5.669106e+01
## [1166] 4.409402e+00 9.046239e+00 1.760595e+00 3.415489e+00 2.610995e+01
## [1171] 3.327034e+01 1.241930e+01 1.218154e+00 2.762479e+01 4.487659e-01
## [1176] 2.845136e+00 2.627329e+00 3.056428e+00 1.460200e+00 8.198108e-01
## [1181] 2.278788e+01 2.298215e+01 5.397180e+00 5.086645e+00 1.951616e+00
## [1186] 6.367671e+00 7.983956e+00 1.482919e+00 8.624564e+00 1.291741e+01
## [1191] 4.327243e+00 8.912183e+01 4.696410e+00 2.871812e+01 1.058131e+01
## [1196] 2.098064e+01 1.746438e+00 1.117896e+01 7.224309e+00 1.667294e+01
## [1201] 4.003440e+00 2.179914e+01 1.516481e+01 9.319746e+00 1.432981e+01
## [1206] 9.651904e+00 1.121309e+00 2.114617e+01 3.870188e+01 2.401089e+01
## [1211] 1.366999e+01 2.263255e+01 7.156296e+00 9.225732e-01 3.303665e+00
## [1216] 6.216424e+00 4.918147e+00 3.119707e+01 6.884342e+00 1.324794e+01
## [1221] 2.288705e+01 4.738830e+01 2.699424e+01 7.714072e+00 3.214058e+01
## [1226] 1.337022e+01 2.148271e+00 9.021157e+00 4.990794e+01 2.117123e+00
## [1231] 9.043724e-01 2.098800e+01 1.610576e+01 1.121367e+01 2.612189e+01
## [1236] 1.577548e+01 8.718416e+00 2.480954e+00 8.921415e+00 1.798800e+01
## [1241] 9.319835e+00 3.439693e+01 1.437939e+01 3.233260e+00 4.957525e+01
## [1246] 3.700044e+00 1.143426e+01 1.858527e+00 7.476548e+00 3.537167e+00
## [1251] 7.346976e+00 4.617653e+01 2.832843e+01 1.468541e+00 8.706947e-01
## [1256] 3.206722e+00 1.825859e+01 4.681775e+01 2.578049e+00 1.062925e+00
## [1261] 1.219538e+01 8.488695e+00 1.103498e+00 7.514002e+00 1.972407e+01
## [1266] 7.949642e+00 2.702182e+01 1.529291e+01 3.180198e+01 3.721929e-01
## [1271] 2.459455e+00 3.439780e+01 1.615621e+00 1.729128e+01 9.035217e+00
## [1276] 9.409360e-02 1.012873e+01 5.138618e+00 4.773501e+00 6.616633e+00
## [1281] 1.602048e+01 2.522570e+01 1.328558e+01 1.654434e+01 4.884370e+00
## [1286] 6.439954e+00 1.599080e+01 2.880962e+00 2.108285e+01 9.801579e+00
## [1291] 3.578431e+00 4.193149e+00 9.931576e+00 5.549393e+01 1.429015e+01
## [1296] 2.244045e+00 6.801868e+00 4.738632e-01 1.284753e+01 1.394915e+01
## [1301] 2.352825e+01 1.206502e+01 2.647385e+01 2.918701e+00 9.399256e+00
## [1306] 1.169517e+01 7.714899e+01 3.590661e+01 1.254107e+01 3.209637e+01
## [1311] 1.006327e+02 2.321274e+01 3.518758e+00 2.596427e+01 8.050471e+00
## [1316] 5.396290e+00 4.131041e+00 2.058976e+01 9.028943e+00 1.434939e+01
## [1321] 1.206106e-02 2.894831e+00 7.320270e+00 2.758972e+01 4.526159e-01
## [1326] 2.289990e+01 1.167412e+01 1.049648e+01 3.944722e-02 1.912486e+01
## [1331] 1.533249e+01 5.015360e+00 6.896063e+00 1.754583e+00 1.728739e+01
## [1336] 2.784595e+01 1.167230e+01 1.519148e+01 1.087662e-01 7.723114e+00
## [1341] 2.903922e+00 1.761268e+01 1.772507e+01 2.184127e+01 8.658601e+00
## [1346] 1.900617e+01 1.399352e+01 1.843690e+01 3.539834e+01 9.515513e+00
## [1351] 6.452203e+00 2.686566e+01 1.274783e+01 5.294508e+00 1.700045e+00
## [1356] 5.048739e+00 1.196534e+01 8.064065e+00 4.391754e+00 3.036122e+00
## [1361] 3.715605e+01 2.192355e+01 1.687455e+00 1.222749e+00 2.617386e+01
## [1366] 4.349757e+00 1.031083e+01 4.038989e+00 1.668141e+01 4.743833e+00
## [1371] 1.670745e+01 1.272366e+01 1.233207e+00 1.555375e+01 1.423545e+01
## [1376] 7.686172e-01 4.211985e+01 1.631991e+01 1.352491e+01 2.016694e+00
## [1381] 6.266578e+00 2.868531e+01 6.334363e+00 1.160620e+01 2.524160e+00
## [1386] 1.318294e+01 1.617332e+01 4.885637e+00 1.686484e+01 2.443586e+00
## [1391] 7.661641e-01 2.476134e+01 1.166865e+00 1.403726e+00 1.147650e+01
## [1396] 2.343881e+01 4.357141e+00 2.446097e+00 2.045797e+01 8.979672e+00
## [1401] 1.781789e+01 1.170914e+01 9.911198e+00 2.445020e+01 1.767843e+00
## [1406] 2.582994e+00 4.053410e+01 3.242515e+00 1.944143e+01 6.595850e+00
## [1411] 9.722794e-01 2.627238e-01 1.405950e+01 8.152456e+00 8.809138e-01
## [1416] 2.275672e+01 2.781122e+00 3.617057e+00 9.715949e+00 1.207199e+01
## [1421] 2.201182e+00 1.590063e+01 7.729856e+00 7.366712e-01 1.661722e+01
## [1426] 4.365141e+00 1.836734e+00 5.413357e+00 1.071312e+00 1.748597e+01
## [1431] 2.179668e+01 1.422051e+01 1.777688e+01 8.940630e+00 1.065218e+01
## [1436] 3.846398e+00 1.946315e+01 1.270648e+01 4.917218e+00 6.500842e+00
## [1441] 4.008400e+00 1.350394e+01 4.330359e+00 1.773666e+01 1.287188e+01
## [1446] 4.813339e+00 2.222362e+01 9.259035e+00 1.729353e+00 1.219859e+01
## [1451] 9.237376e+00 1.315887e+01 2.635467e+01 1.223633e+01 2.458252e+01
## [1456] 4.158364e+00 1.415513e+01 5.876595e-01 1.859982e+00 3.660762e+01
## [1461] 1.445045e+00 5.856123e+00 1.439960e+01 1.084693e+01 1.076748e+01
## [1466] 1.320352e+01 3.498348e+01 4.491410e+00 6.594417e+00 3.130803e+00
## [1471] 1.848378e+00 2.164587e+01 1.348153e+00 1.098180e+01 1.974332e+01
## [1476] 5.848619e+00 1.515076e+01 6.717228e+00 7.623881e+00 6.629078e+00
## [1481] 1.217712e+00 4.197507e+00 2.038862e+01 8.931608e+00 3.369729e+01
## [1486] 7.496376e+00 9.157390e+00 2.529559e+00 1.012959e+01 1.549973e+00
## [1491] 3.352401e+00 4.942288e+00 1.368173e+01 1.363545e+01 1.548896e+01
## [1496] 3.046954e+01 3.249306e+01 8.779774e+00 1.949943e-01 1.232498e+01
## [1501] 5.704955e+00 2.055973e+01 2.229246e+00 9.592268e+00 8.357066e+00
## [1506] 6.329716e+00 1.271567e+01 8.347400e+00 1.715494e+01 5.986726e+00
## [1511] 1.949598e+00 1.838534e+00 4.198351e+00 3.960325e+01 3.674028e+01
## [1516] 5.890098e+00 3.687521e+00 2.554977e+01 2.292888e+00 1.056124e+01
## [1521] 3.587357e+00 6.434074e+00 5.801329e+00 2.393899e+00 2.128547e+00
## [1526] 7.175905e+00 1.486191e+01 1.630541e+01 6.165692e+00 1.265810e+01
## [1531] 2.941474e+00 5.939535e+00 5.488544e+01 5.482128e-01 1.239089e+01
## [1536] 5.641659e+00 1.164659e+01 6.051033e-02 2.028611e+01 1.262831e+01
## [1541] 1.152113e+01 2.569770e+01 1.879515e+01 1.377315e+01 1.797760e-01
## [1546] 3.208320e+01 4.060023e+01 2.904522e+00 1.208465e+01 1.985846e+01
## [1551] 1.771208e+01 1.232541e+01 1.629861e+01 1.898154e+01 1.239406e+01
## [1556] 1.205792e+01 4.073244e+01 2.605640e+00 1.092341e+01 1.240148e+01
## [1561] 6.755241e+01 1.383993e-01 7.981858e+00 1.410248e+01 1.504685e+01
## [1566] 4.157233e+00 2.619741e-01 2.635002e+00 1.728489e+01 1.668110e+01
## [1571] 1.274310e+01 2.297329e+01 7.117357e+00 1.914271e+00 7.445639e+00
## [1576] 1.286507e+01 7.219744e-01 5.697943e+00 1.116374e+01 1.482320e+00
## [1581] 1.933219e+00 5.965020e+00 1.136663e+01 3.518575e+01 1.489483e+01
## [1586] 1.817938e+01 1.404510e+01 5.890926e+00 7.582769e+00 7.533243e+00
## [1591] 1.666218e+00 9.916413e+00 5.101872e+00 1.812639e+01 8.089126e+00
## [1596] 6.801281e+00 2.263967e+01 1.358590e+01 1.741198e+00 1.018105e+01
## [1601] 4.169089e+00 3.353135e+00 3.976453e+00 2.678686e+01 6.259531e+00
## [1606] 1.608036e+01 7.339790e+00 1.921412e+00 1.026989e+01 7.618367e+00
## [1611] 2.547079e+01 2.732175e-01 2.550861e+01 1.533312e+00 1.671966e+01
## [1616] 2.480799e+01 4.146126e+00 2.146988e+00 5.435050e+00 6.193585e+00
## [1621] 8.087310e+00 3.358136e+00 2.242291e+00 3.730617e+01 4.805720e+00
## [1626] 3.323984e-01 1.604322e+01 3.858028e+01 8.466196e-01 7.343393e-02
## [1631] 2.029722e+01 1.294372e+00 2.203530e+00 3.084149e+00 3.906535e+00
## [1636] 1.480415e+01 7.391447e+00 1.190780e+00 2.781859e+01 1.363548e+01
## [1641] 2.854737e+01 1.994185e+01 5.153472e+00 5.785338e+00 4.946406e+00
## [1646] 2.068742e+01 6.568495e+00 4.627843e+00 7.295530e+00 7.546641e+00
## [1651] 1.082062e+01 5.371478e+00 2.279875e+00 5.623149e-01 1.956715e+01
## [1656] 1.184089e+01 1.580320e+01 7.643166e+00 1.330817e+00 3.460223e-01
## [1661] 1.755952e+01 5.833585e+00 3.353031e-01 1.466039e+01 6.466102e+00
## [1666] 5.133218e-02 4.201541e+00 2.632696e+01 1.555824e+00 4.276089e-01
## [1671] 2.180775e+01 3.179596e+01 5.218362e+00 5.244771e+00 2.744350e+01
## [1676] 6.380454e+00 1.955148e-01 1.302891e+00 3.410438e+01 2.277630e+01
## [1681] 1.358549e+01 8.384677e+00 3.710300e+01 1.929423e+01 4.247423e+00
## [1686] 3.252620e+00 2.138896e+01 5.919987e+00 2.341779e+01 6.591125e+00
## [1691] 1.696303e+00 7.809597e+00 2.996093e+00 2.307655e+01 1.249387e+01
## [1696] 1.519566e-01 1.355590e+00 5.869990e+00 2.379122e+01 1.907377e+00
## [1701] 8.242136e+00 5.349333e+00 1.200843e+00 7.796044e+00 1.432499e+01
## [1706] 5.426141e-02 6.509076e-01 7.838082e+00 3.800766e+00 3.781167e+00
## [1711] 7.171015e+00 1.481026e+01 4.114624e+00 8.029042e+00 2.983647e+01
## [1716] 4.276288e+00 1.523496e+01 3.873695e+00 2.572612e+00 3.471447e+01
## [1721] 7.167150e+00 2.035839e+01 1.060078e+00 1.578191e+00 2.854103e+01
## [1726] 1.893131e+00 4.909186e+00 1.681673e+01 3.446169e+00 4.801552e+00
## [1731] 1.877028e+01 9.797577e+00 1.165192e+00 6.825803e+00 1.460021e+01
## [1736] 2.443503e+01 2.535584e+00 8.251168e+00 4.585903e+01 3.138621e+01
## [1741] 1.756038e+00 2.853799e+01 3.083919e+00 1.412757e+01 3.007532e+01
## [1746] 1.548460e+01 2.776770e+01 2.419394e+01 2.047848e+01 6.093219e-01
## [1751] 1.379451e+01 3.313262e+01 1.244717e+01 2.416579e+00 7.633074e+00
## [1756] 6.113054e+00 1.780576e+01 1.225880e+01 1.239027e+01 6.941010e+01
## [1761] 4.085111e+00 2.949939e-01 1.397534e+01 1.699386e+01 5.900904e+00
## [1766] 1.245688e+01 3.007722e+00 4.289909e+00 3.588125e+01 2.678671e+00
## [1771] 1.337854e+01 3.610014e+00 6.860582e+00 1.333468e+01 2.460717e+01
## [1776] 1.123113e+01 6.334926e+00 3.654809e+00 2.545586e+01 7.972521e+00
## [1781] 4.850237e+00 7.157136e+00 6.781059e+00 2.252281e+00 1.051697e+01
## [1786] 1.799444e+01 5.780244e+00 4.575918e+00 8.593602e-01 1.832515e+01
## [1791] 1.272950e+01 6.030336e+00 5.746466e+00 1.163647e+00 3.052504e-01
## [1796] 2.286151e+01 3.628334e+00 9.716687e+00 2.700675e+01 6.580781e+00
## [1801] 1.269502e+00 3.556559e+00 3.516731e-01 2.165718e+00 1.174528e+01
## [1806] 1.339237e+00 1.645211e+01 7.158453e+00 9.551476e+00 1.213754e+01
## [1811] 6.241387e+00 8.510532e+00 4.590697e+00 1.322497e+00 1.752546e+00
## [1816] 1.816532e+01 1.663226e+01 2.456957e-01 1.157802e+00 4.361814e+00
## [1821] 9.771032e-02 4.197523e+01 1.125329e+01 2.110669e+01 7.345565e+00
## [1826] 2.556170e+01 4.689680e+00 4.342164e+00 1.920111e+01 1.264871e+01
## [1831] 4.024048e+00 3.718546e+00 3.066756e+01 2.444727e+01 4.281037e+00
## [1836] 2.395387e+01 1.880814e+00 8.950404e+00 2.211445e+01 8.867882e+00
## [1841] 2.147143e+01 1.666954e+01 6.001770e+00 8.776022e-01 9.384255e-02
## [1846] 1.383671e+01 4.879499e+00 4.068686e+00 5.208978e+01 2.333393e+01
## [1851] 5.099449e+00 1.118690e+01 3.083447e+01 1.104720e+01 2.847371e+00
## [1856] 3.636788e+00 1.626948e+01 2.924109e+00 1.479145e+00 2.155347e+00
## [1861] 8.112738e+00 8.081107e+00 3.823409e+00 9.501682e+00 6.787483e+00
## [1866] 5.796653e+00 1.683998e+01 1.185650e+01 1.000168e+00 5.760013e+00
## [1871] 1.150775e+01 1.868276e+01 2.604274e+01 4.391672e+00 1.808946e+00
## [1876] 1.417694e+01 1.652440e+01 1.327087e+01 7.608855e-01 5.144597e+00
## [1881] 3.533789e+01 2.536153e+01 8.706634e+00 5.690589e+00 1.252713e+01
## [1886] 5.790555e+00 1.408285e+01 1.960387e+00 2.969695e+01 6.181994e-01
## [1891] 1.908386e+01 6.781925e+00 1.045421e+01 1.830923e+00 3.459521e-01
## [1896] 3.723387e+00 3.054626e+00 1.982168e+01 3.093621e+01 1.716655e+00
## [1901] 4.120772e+01 6.337664e-01 6.384530e+01 1.025951e+01 1.371669e+01
## [1906] 2.699972e+00 4.995718e+00 3.658488e+00 1.724615e+01 1.074245e+01
## [1911] 5.720501e+00 1.187526e+00 1.078569e+01 5.882603e+00 9.925880e+00
## [1916] 1.614044e+01 3.899972e+00 8.399278e+00 1.658138e+01 7.503306e+00
## [1921] 3.555038e+01 2.389206e+01 4.519783e+00 1.228494e+01 2.143528e+00
## [1926] 2.077893e+01 9.028982e+00 1.946173e+01 1.086679e+01 9.642675e+00
## [1931] 1.697570e+00 1.248269e+01 1.427872e+01 7.064925e+00 5.373268e+00
## [1936] 8.381340e+00 1.002171e+01 5.309290e+00 9.991831e+00 6.865385e+00
## [1941] 1.487431e+01 4.484571e+00 2.257560e+00 2.175660e+00 2.541060e+00
## [1946] 8.253427e+00 1.233452e+01 5.662681e+00 1.249206e+01 2.700446e+01
## [1951] 4.766923e+00 3.697944e+00 1.051653e+01 4.730176e-01 3.856280e+00
## [1956] 5.615368e+00 5.411861e+00 4.089925e+01 1.248427e+01 1.836511e+00
## [1961] 1.434283e+01 8.988668e+00 7.237429e+00 1.475843e+01 3.942537e+00
## [1966] 4.573762e+00 2.973845e+01 2.460053e+00 7.847041e-01 2.389459e+01
## [1971] 1.849216e-01 4.803270e+00 6.032318e+00 8.566215e+00 3.513665e+00
## [1976] 2.344872e+01 2.939306e-01 3.134755e+00 2.033050e+01 1.002580e+01
## [1981] 2.259896e+00 1.850266e+01 8.546708e+00 2.921388e+00 7.289202e-03
## [1986] 4.117702e+00 2.412136e-01 3.333031e+01 1.069162e+01 2.410343e+00
## [1991] 7.493814e+00 1.110009e+01 1.286521e+01 8.305085e+00 1.134771e+01
## [1996] 1.027469e+01 2.578405e+01 2.085471e+01 2.565526e+01 2.655240e+00
## [2001] 1.390076e+01 1.516025e+00 2.012707e+00 1.468787e+01 9.832231e+00
## [2006] 2.668237e+00 3.198511e+00 1.131524e+01 2.927695e+01 6.941530e+00
## [2011] 1.033138e+01 2.572960e+00 3.526965e+00 6.430692e+00 1.290340e+01
## [2016] 2.090277e+01 8.582797e-01 2.004614e+01 2.778631e+00 1.580218e+01
## [2021] 1.799791e+01 1.244662e+00 3.488135e+00 2.083949e+00 3.081338e+00
## [2026] 5.393270e-01 1.864151e+00 1.993657e+01 3.048635e+01 1.958596e+00
## [2031] 8.600799e+00 7.807041e+00 8.571900e+00 1.485245e+01 3.791482e+00
## [2036] 1.809915e+01 4.734533e+01 3.416996e+01 8.588135e+00 6.703108e-01
## [2041] 2.557774e-01 1.936365e+00 4.505002e+00 3.965774e+01 7.476581e+00
## [2046] 5.824492e-01 5.922674e+00 8.379857e+00 5.978428e+00 1.319601e+00
## [2051] 1.394176e+01 1.826829e+00 9.132665e+00 3.906678e+00 1.094010e+01
## [2056] 5.269763e+01 4.910611e+00 7.130644e+01 9.690771e+00 1.448974e+01
## [2061] 4.515158e+01 6.135281e+00 7.803777e+00 1.614530e+01 4.665357e+00
## [2066] 9.482117e+00 8.226872e+00 7.191838e+00 2.752104e+01 2.230211e+01
## [2071] 2.380145e+01 3.115804e+01 7.403110e+00 3.356875e+00 3.903533e+00
## [2076] 1.991378e+00 2.998732e-02 3.756717e-01 1.751293e+00 1.114221e+01
## [2081] 8.595904e+00 5.848048e+00 1.246021e+01 1.378772e+01 1.571238e+01
## [2086] 3.659971e+01 1.044718e+01 2.576883e+01 1.412099e+01 2.104198e+00
## [2091] 7.242006e-01 1.907947e+00 2.764297e+00 1.735130e+01 3.469606e+00
## [2096] 1.461017e-01 9.439923e+00 6.449195e+01 5.563655e-01 6.438060e+00
## [2101] 2.067030e+01 9.045220e+00 9.307666e+00 8.093044e+00 7.084091e+00
## [2106] 2.665474e+01 2.352543e+01 2.464875e+01 7.046133e+00 4.501643e-01
## [2111] 2.293762e+01 1.779915e+00 2.559629e+00 1.078928e+01 1.038059e+01
## [2116] 1.625939e+01 2.851923e+00 1.153624e+01 4.213866e+00 1.093071e+00
## [2121] 1.530335e+01 1.436583e+01 1.823417e+01 1.577063e+01 5.561964e+00
## [2126] 3.719285e+00 5.794010e+00 2.367134e+01 3.451320e+00 1.285167e+01
## [2131] 3.420616e+01 1.176819e+01 8.373502e+00 5.767707e+00 3.993771e-01
## [2136] 7.008153e-01 1.255465e+01 6.285837e+00 1.343478e+01 2.700190e+01
## [2141] 1.335622e+01 8.444196e+00 7.832507e+00 4.306602e-01 2.394849e+01
## [2146] 3.600826e+00 2.661054e+01 3.018938e+00 4.021699e+01 2.913030e+01
## [2151] 8.283343e+00 1.907514e+01 1.304756e+01 5.460093e+00 3.915489e-02
## [2156] 2.003540e-01 2.708911e+01 4.151728e+00 1.257035e+01 4.046199e+00
## [2161] 1.947282e+01 3.668295e+01 1.587590e+00 6.246325e+00 1.001770e+01
## [2166] 3.269478e+00 2.034976e+01 8.768740e+00 6.263518e+00 7.596507e+00
## [2171] 3.085755e+01 5.547550e+00 1.096991e+01 5.828000e+00 4.781107e+00
## [2176] 1.825212e+00 3.203833e+00 1.311288e+01 1.741056e+01 4.223490e+00
## [2181] 8.849223e+00 1.063110e+01 4.578525e+00 7.154396e-01 1.364180e+01
## [2186] 2.909340e+01 6.567435e+00 3.400152e+00 8.083887e+01 9.122179e+00
## [2191] 3.931124e+00 9.999397e+00 4.444908e+00 9.265898e+00 9.003081e+00
## [2196] 2.153858e-01 2.920089e+01 9.190000e-01 3.213069e+01 1.034543e+01
## [2201] 3.165210e+00 1.169695e+01 2.358413e+01 2.015968e+00 8.417471e+00
## [2206] 1.189390e+01 1.168024e+01 1.969001e+01 3.137783e+00 2.856053e+00
## [2211] 6.430396e+00 3.038331e+01 8.935609e-01 4.497171e+01 6.183931e+01
## [2216] 5.444638e+01 2.238228e+00 7.046097e+00 3.539706e+01 1.314285e+01
## [2221] 2.778456e+01 1.396463e+00 3.556371e+00 2.686199e+00 2.538211e+00
## [2226] 6.060014e+00 1.015787e+00 2.637043e+01 3.371163e+00 3.509146e+00
## [2231] 1.361686e+01 1.643954e+00 1.260411e+01 8.878971e-01 3.542937e+00
## [2236] 2.259882e+01 7.925652e-01 1.476550e+01 6.830464e+00 2.546694e+01
## [2241] 1.019797e+01 9.567008e+00 6.599882e+00 1.320449e+00 1.058707e+01
## [2246] 1.894658e+01 1.446456e+01 1.783245e+01 2.902817e+01 1.051912e+00
## [2251] 8.180422e-01 3.445176e+00 5.196295e+00 6.078985e+00 4.715364e+00
## [2256] 7.961837e+00 1.759097e+00 1.152254e+01 1.218041e+01 9.126616e+00
## [2261] 3.032755e+00 3.351052e+01 2.206854e+00 5.987310e+00 6.827796e+00
## [2266] 1.335030e+00 1.196501e+01 2.380785e+01 5.237014e+00 1.549429e+01
## [2271] 1.017713e+01 2.181850e+01 5.084700e+01 6.099608e+00 1.527317e+01
## [2276] 1.681053e+01 2.715905e+00 3.502150e+01 2.403328e+00 7.826569e+00
## [2281] 5.705354e+00 2.058168e+01 3.288754e+00 5.014054e+00 1.161190e+01
## [2286] 5.450676e+01 7.725744e+00 7.148990e+00 6.515727e+00 9.703849e+00
## [2291] 2.752552e+00 3.414281e+01 2.983915e+00 1.009034e+00 1.538627e+01
## [2296] 1.200295e+01 6.268691e+00 1.667506e+01 2.938742e+00 9.614718e+00
## [2301] 1.354399e+01 3.385004e+00 2.934629e+00 2.733077e+01 2.674089e+01
## [2306] 2.398520e+00 3.655764e+00 6.564304e+00 1.680807e+00 9.508653e+00
## [2311] 6.973680e+00 5.307937e+01 1.332900e+01 1.145956e+01 2.510731e+01
## [2316] 1.297361e+01 1.147632e+01 1.367181e+01 1.165202e+01 1.788463e+01
## [2321] 3.446356e+01 1.738456e+01 1.815513e+01 1.058388e+01 4.922458e-01
## [2326] 1.037748e+01 1.395404e+01 9.405109e+00 5.413278e+00 2.571171e+01
## [2331] 1.101915e+01 1.310144e+01 1.740889e+01 1.846096e+00 3.353865e+00
## [2336] 6.264210e+00 5.882208e+00 2.984350e+01 1.893686e+01 1.045567e+01
## [2341] 2.429574e+00 6.847961e+01 3.380551e+00 1.428328e+01 4.811495e+00
## [2346] 1.111040e+01 1.407492e+00 1.539319e+01 1.588170e+01 8.558266e+00
## [2351] 2.388678e+00 1.103728e+00 2.836497e-01 1.415116e+01 1.259777e+00
## [2356] 3.706287e+00 6.289281e+00 4.758002e+00 1.923890e+01 7.671948e+00
## [2361] 1.223223e+00 2.970997e+01 9.348457e-01 6.294477e+00 1.272207e+01
## [2366] 4.422826e-01 5.516691e+01 7.371044e+00 1.102592e+01 6.452811e+00
## [2371] 1.527429e+01 5.585709e+01 2.481826e+01 1.032978e+01 8.540151e+00
## [2376] 1.325727e+00 2.484751e+01 4.302069e+00 9.417416e-01 6.742769e+00
## [2381] 5.993836e+00 2.066120e+01 1.136028e+00 8.856780e+00 3.614577e+00
## [2386] 5.110806e+00 1.203998e+01 2.404365e+00 3.279815e+01 2.711496e+00
## [2391] 7.612476e+00 3.723082e+00 4.353574e+00 6.302559e+00 7.388706e+00
## [2396] 1.593209e+01 9.206535e+00 1.508542e+01 9.971184e+00 2.392356e+01
## [2401] 1.132680e+01 3.326579e+00 3.983727e+00 7.015677e+00 2.091669e+00
## [2406] 1.352013e+01 3.806047e+01 1.563996e+01 2.635708e+01 3.810249e+00
## [2411] 4.737076e+00 2.991417e+01 1.151738e+01 2.354954e+01 3.023634e+00
## [2416] 4.376723e+00 5.286549e+01 8.088451e+00 2.782450e+01 1.446791e+01
## [2421] 1.989204e+00 1.030544e+01 6.780265e-01 3.179006e+01 1.016776e+01
## [2426] 1.517974e+00 4.228055e+01 2.286006e+00 3.267666e+00 3.027163e+01
## [2431] 1.122860e+01 1.786252e+00 2.749987e+01 2.036122e+00 9.351482e+00
## [2436] 1.355510e+00 3.003913e+00 1.073659e+00 3.057731e+00 5.953215e+00
## [2441] 8.454776e+00 2.369710e+01 2.764103e+00 1.112331e+01 5.320596e+00
## [2446] 1.208464e+00 3.635927e+01 1.869502e+01 2.460041e+01 1.484597e+01
## [2451] 1.280639e+01 1.972378e+01 1.790492e+00 6.525811e+00 5.364715e+00
## [2456] 5.916313e+00 1.768437e+01 5.520871e+00 1.831394e+00 1.138113e+01
## [2461] 1.048753e+01 2.141115e+01 3.240260e+00 9.237245e-02 5.224300e+01
## [2466] 2.956442e+01 9.769113e+00 8.299296e+00 4.459685e+00 4.245916e-01
## [2471] 3.720347e+00 1.463535e+00 1.488992e+01 2.791303e+01 1.160376e+01
## [2476] 2.982511e+01 6.959595e+00 1.244174e+01 2.331656e+01 6.759536e+00
## [2481] 1.056527e+00 1.259064e+01 8.477842e+00 4.765844e+00 2.259496e+01
## [2486] 3.365391e+01 9.496469e+00 1.279470e+00 2.265987e+01 1.560636e+00
## [2491] 6.960620e+01 8.740018e+00 1.066994e+01 4.868155e+00 2.755477e+00
## [2496] 1.522300e+01 9.574249e+00 3.835976e+01 1.392331e+01 1.447359e+01
## [2501] 9.922408e-01 8.648890e+00 1.639073e+00 4.976665e+00 3.631312e+00
## [2506] 4.025641e+01 1.676958e+01 6.081459e+00 7.999109e+00 1.507051e+00
## [2511] 8.863382e+00 4.778210e+00 1.228333e+01 5.639365e+00 2.402975e+01
## [2516] 5.728249e+00 5.909348e-01 1.233033e+01 2.209258e+00 6.114478e+00
## [2521] 4.574326e+00 1.460767e+01 5.146325e+00 9.533398e+00 9.138450e+00
## [2526] 2.094501e-01 6.021358e+00 6.762586e+01 6.844784e+00 2.319832e+01
## [2531] 1.190606e+01 1.684996e+01 3.753991e+00 4.635083e+00 1.747010e+01
## [2536] 9.292979e+00 6.270449e+00 7.750595e+00 2.984344e+01 5.229613e+00
## [2541] 4.037338e+00 9.392137e-01 2.155011e+01 4.169617e+00 1.738136e+00
## [2546] 4.290935e+00 3.477284e+01 6.110422e+00 7.758467e+00 1.340918e-02
## [2551] 5.579382e+00 7.948895e-01 2.400349e+01 2.181758e+01 1.458820e+01
## [2556] 1.835804e+00 1.901119e+01 2.769934e+01 1.313026e+00 7.093532e+00
## [2561] 3.629244e+01 1.395099e+00 3.283458e+00 2.127911e+01 9.218619e-01
## [2566] 1.709422e+01 3.491711e+01 2.086068e+01 1.976608e+01 4.913825e+00
## [2571] 2.089366e+01 4.645545e+00 3.134752e+01 1.465855e+01 2.353998e+01
## [2576] 4.641038e+00 8.838566e+00 1.196315e+01 1.098938e+01 4.936172e+00
## [2581] 2.005944e+01 3.103470e+00 1.500919e+01 3.958291e+01 2.037878e+01
## [2586] 6.597484e-01 2.825168e+00 1.153390e+01 1.357914e+01 2.514233e+01
## [2591] 2.276538e+01 3.173597e+01 2.658769e+00 4.028110e+01 4.929030e+00
## [2596] 1.262242e+01 1.643989e+01 1.005412e+01 1.436308e+01 1.401796e+01
## [2601] 8.182912e+00 1.697751e+00 1.063541e+01 1.458148e+01 4.483835e+01
## [2606] 1.366085e+01 2.064032e+00 1.057758e+01 8.189337e+00 7.868893e+00
## [2611] 8.083281e+01 1.694950e+01 4.867620e+00 1.527026e+00 1.135690e+00
## [2616] 1.163961e+00 6.256037e+00 3.910576e+01 3.250739e+00 6.063498e-01
## [2621] 2.622652e+01 7.761131e+00 2.551744e+00 2.509041e+00 8.831398e-01
## [2626] 1.453852e+01 1.077919e+01 1.269972e+01 5.294360e+00 1.867364e+00
## [2631] 9.437114e+00 2.086201e+01 4.480916e+01 2.376174e+00 5.302200e+00
## [2636] 1.149130e+01 2.585096e+01 6.068587e+00 3.454156e+00 2.139503e+01
## [2641] 3.485682e+00 5.256062e+00 1.775855e+00 4.349989e+01 2.400385e+00
## [2646] 8.395912e+00 2.453068e+00 1.531528e+01 4.660773e-02 2.172336e+01
## [2651] 1.713413e+01 2.483552e+00 2.192779e+01 2.981408e+00 7.199385e-01
## [2656] 2.708801e+00 1.831485e+01 4.035377e+00 1.259616e+01 1.413420e+01
## [2661] 6.672632e+00 1.728903e+01 4.206743e+00 2.455388e+00 4.098113e+00
## [2666] 4.901014e+01 8.987003e+00 9.156041e+00 1.338316e+00 2.968995e-02
## [2671] 7.516100e+00 3.805337e+01 1.256630e+01 1.026822e+01 1.237154e+01
## [2676] 2.542527e+01 4.042273e+01 6.706932e+00 1.099036e+01 1.761321e+01
## [2681] 2.860043e+01 1.053562e+00 1.866203e+01 5.989877e+00 7.464686e+00
## [2686] 6.877769e+00 9.250205e+00 2.871905e+00 9.745521e-01 1.608356e+00
## [2691] 1.642051e+00 3.183674e+01 1.268091e+01 1.593791e+00 5.871361e+00
## [2696] 1.377542e+00 1.050982e+01 1.372633e+01 2.042871e+01 4.338721e+00
## [2701] 3.285159e+01 5.338823e+00 6.877773e+00 6.000918e+00 4.561129e-01
## [2706] 4.205517e+00 4.601489e+01 8.693916e+00 4.931948e+00 1.489188e+01
## [2711] 6.262078e+00 2.184703e+01 9.613916e+00 7.421888e+00 1.867898e+01
## [2716] 3.824794e-01 3.491180e+00 3.799908e+01 7.807442e-01 1.215352e+00
## [2721] 1.895261e+00 1.023515e+01 1.915545e+00 3.516401e+01 3.042588e+00
## [2726] 8.065415e+00 4.792213e+00 2.612199e+00 5.760339e+00 1.154054e+01
## [2731] 1.575104e+01 3.806917e+00 2.393675e+01 1.256802e+00 1.216200e+00
## [2736] 1.620865e+00 5.550443e+00 1.046713e+01 2.499475e+00 3.870117e+00
## [2741] 4.950822e+00 2.605011e+00 6.156693e+00 1.840541e+01 5.852896e+00
## [2746] 1.144265e+01 7.750180e-01 1.513476e+01 3.656090e+00 8.131687e+00
## [2751] 4.954033e+01 1.785277e+01 4.452500e+00 2.329278e+01 1.084878e+01
## [2756] 2.344959e+00 9.227826e-01 3.737315e+01 7.939687e+00 9.283128e+00
## [2761] 2.236070e+00 1.331614e+01 3.363614e+00 4.240474e+00 4.368745e+00
## [2766] 1.340471e+01 3.046023e+01 1.374580e+01 4.594407e+00 1.088657e+01
## [2771] 4.509687e+00 1.503658e+01 1.898047e+01 8.084303e+00 4.711521e+01
## [2776] 2.778529e+00 2.005782e+01 1.112417e+01 1.563595e+01 1.071273e+01
## [2781] 6.988107e+00 3.866577e+01 1.228456e+01 5.485460e+00 2.519120e+01
## [2786] 7.045890e+00 1.301633e+00 1.482105e+01 4.845427e+00 6.424303e+01
## [2791] 2.186888e+01 2.751342e+01 1.639009e+00 3.884838e+00 2.949115e+00
## [2796] 2.294967e+01 2.110206e+01 1.397169e+01 6.771586e+00 1.726738e+00
## [2801] 1.750839e+01 3.073365e+00 6.191849e+00 6.198823e+00 4.802886e+00
## [2806] 1.042693e+01 2.068204e+00 2.050080e+00 1.014294e+01 8.410711e+00
## [2811] 6.453207e+00 3.488590e-01 6.078820e-01 1.049744e+01 1.040666e+01
## [2816] 2.058133e+01 4.583877e-01 3.414093e+01 3.137838e+01 4.365020e-02
## [2821] 4.619620e-01 1.692225e+00 9.128914e-01 4.526049e+00 1.585264e+00
## [2826] 6.154051e-01 5.892948e+00 7.866541e+00 2.894551e+00 1.582402e+00
## [2831] 9.284322e+00 2.055916e+01 4.835392e+00 1.746460e+01 2.990356e+00
## [2836] 1.448367e+01 2.451462e+00 9.629525e-01 3.939495e+01 2.320925e+01
## [2841] 1.257391e+01 6.427524e+01 2.778933e+00 6.963410e+00 3.581575e+01
## [2846] 1.340198e+01 5.854307e+00 1.553793e+01 3.037438e+00 1.685306e+01
## [2851] 6.244364e+00 3.543119e+01 2.111110e+01 1.722714e+01 5.407990e+00
## [2856] 1.158744e+00 3.004501e+01 7.404770e-02 6.417818e+00 2.395800e+01
## [2861] 1.517468e+01 2.167882e+00 6.116627e+00 2.294696e+00 2.928990e+01
## [2866] 1.132255e+01 2.486696e+01 4.224688e+00 1.186920e+01 1.277159e+01
## [2871] 5.822321e+00 7.492799e+00 5.434298e+00 3.771692e+00 4.522791e-01
## [2876] 9.640649e+00 4.339343e+00 5.825467e+01 5.425448e+00 1.670617e+00
## [2881] 1.622387e+01 1.517050e+01 4.655405e+01 2.970532e+01 1.255592e+01
## [2886] 4.159806e+01 5.619968e+00 2.693288e+00 3.274517e+01 7.779699e-01
## [2891] 2.615822e+00 1.107660e+01 2.014620e+01 1.250763e+01 2.190072e+00
## [2896] 3.607333e+00 1.540754e+01 1.602253e+01 2.578522e-01 5.072252e+01
## [2901] 2.810034e+00 8.358821e+00 1.678052e+00 8.975681e+00 2.610377e+00
## [2906] 1.260497e+01 2.364881e+01 2.840290e+00 4.285221e+00 1.978182e+01
## [2911] 9.583988e+00 1.650763e+01 2.443100e-01 1.527360e+01 2.418833e+01
## [2916] 1.781636e+00 6.155432e+00 1.088800e+00 8.851262e+00 3.558024e+00
## [2921] 1.824843e+01 7.741191e+00 2.986808e+00 1.822802e+00 1.384678e+01
## [2926] 1.845745e+01 3.469488e+01 3.391691e+00 1.230245e+01 3.041583e+01
## [2931] 1.707389e+01 1.646474e+01 9.158842e+00 2.200684e+00 2.977438e+01
## [2936] 3.012163e+00 2.535787e+01 3.552980e-01 2.248711e+00 3.175286e+00
## [2941] 2.548952e+01 3.178394e+01 7.511687e+00 2.813835e+01 2.738811e+00
## [2946] 4.184787e+00 1.678064e+01 8.589614e+00 2.140632e+00 1.158115e+01
## [2951] 5.426489e+00 4.996954e+00 1.316629e+01 1.392604e+01 6.723419e+00
## [2956] 1.903554e+01 4.819615e+00 4.663784e+00 7.683313e+00 2.345778e+01
## [2961] 1.185030e+00 3.499024e+01 5.449994e+01 2.231051e+00 3.066579e+01
## [2966] 1.990863e+01 1.928975e+01 1.027890e+01 7.857620e+00 1.579431e+00
## [2971] 4.162346e+00 5.928153e+00 5.752675e+00 1.575145e+01 7.768280e+00
## [2976] 5.555721e-01 1.952566e+01 7.373259e+00 2.708698e+01 2.808876e+01
## [2981] 3.978057e+01 4.217186e+00 1.265335e+01 5.635476e+00 3.981820e+01
## [2986] 5.756146e+01 3.532352e+01 1.401501e+01 5.576263e+00 2.628319e-01
## [2991] 1.991535e+01 8.156689e+00 1.461564e+01 2.287315e+00 1.204192e+00
## [2996] 1.896231e+01 1.252734e+01 2.334653e+00 2.115906e+01 4.447688e+01
## [3001] 9.852490e+00 7.918270e+00 2.828436e+01 4.729921e+00 5.908411e+00
## [3006] 6.364931e-01 7.484972e+00 3.100936e+01 3.329451e+00 1.170524e+01
## [3011] 3.199720e+00 1.161558e+01 1.130921e+01 3.469322e+00 1.460993e+01
## [3016] 4.630224e+00 2.472741e+01 3.350708e+00 1.104697e+01 2.407539e+01
## [3021] 7.136139e+01 9.451317e+00 3.779026e+01 3.343857e+01 2.978254e+01
## [3026] 2.139548e+01 2.025823e+01 3.527338e-01 1.749737e+01 4.707753e+00
## [3031] 1.354413e+01 2.597495e+01 7.045768e+00 4.846781e+00 4.284465e+00
## [3036] 1.811578e+01 3.206914e+01 2.878939e+01 4.020932e+00 5.716135e+00
## [3041] 2.104960e+01 2.403240e+00 1.418116e+01 1.220771e+00 6.787351e+00
## [3046] 1.348776e+01 4.285305e+00 8.178060e-01 6.398743e+00 3.064228e+00
## [3051] 6.297018e+00 1.287913e+00 3.438800e+00 6.303093e-01 5.183105e+00
## [3056] 2.093181e+01 7.907088e+00 1.575804e+01 3.197308e+00 1.127539e+00
## [3061] 2.352539e+01 1.457955e+01 1.014923e+01 2.397569e-01 1.200350e+01
## [3066] 1.808817e+01 3.440186e+01 6.496002e+00 9.684426e+00 7.358562e+00
## [3071] 5.620882e+00 1.749285e+01 1.562022e+01 1.288601e+01 5.262929e+00
## [3076] 9.227219e+00 1.535082e+01 6.979778e+00 8.816175e+00 2.615242e+01
## [3081] 8.494467e+00 7.975079e+00 3.394878e+00 1.508309e+01 2.247872e+01
## [3086] 2.600643e+01 3.335606e+01 6.092643e+00 2.376596e+01 9.417672e+00
## [3091] 4.828688e+00 7.578170e+00 2.676738e+01 5.653958e+01 2.002300e+01
## [3096] 1.494375e+01 5.334127e+00 1.246946e+00 3.596675e-01 2.254049e+01
## [3101] 2.668625e+00 9.817446e-01 2.392090e+01 1.358328e+01 1.371195e+01
## [3106] 1.446045e+01 2.178379e+00 1.918731e+00 2.338938e+01 6.857236e-01
## [3111] 3.055729e+00 1.097559e+01 8.285300e+00 4.033459e+01 1.687933e+01
## [3116] 7.239434e+00 1.094845e+01 1.591606e+01 1.192179e+01 1.122080e+01
## [3121] 4.700450e+00 2.068424e+01 1.154741e+01 8.206146e+00 2.764896e+01
## [3126] 4.404004e+00 2.025008e-01 5.206385e+01 7.304680e+00 3.499570e-01
## [3131] 4.220823e+00 7.329374e+00 4.636435e+00 1.244760e+01 1.914010e+00
## [3136] 3.715023e-01 3.668327e+00 4.667972e+00 3.726799e+00 1.414013e+01
## [3141] 6.654810e-01 8.575476e-01 1.388238e+01 9.677975e+00 8.055723e+00
## [3146] 8.317501e+00 1.544634e+01 1.867173e-01 2.115702e-01 1.605231e+01
## [3151] 2.734821e+00 3.328031e+01 5.364488e+00 4.603555e+01 5.109955e+00
## [3156] 1.240325e+01 8.488588e+00 4.074804e+00 8.638969e+00 3.124076e+01
## [3161] 1.664431e+00 7.040409e+00 2.300606e+00 1.863246e+01 2.893029e+00
## [3166] 3.409093e+00 8.976420e+00 3.411281e+01 2.321891e+00 2.422059e-01
## [3171] 1.522388e+01 3.148244e+00 2.104338e+00 2.715600e+00 6.430240e+00
## [3176] 2.110730e+01 1.578522e+01 3.334603e+00 6.208063e-01 1.053521e+01
## [3181] 1.514448e+01 3.749758e+00 1.089373e+01 1.154945e+01 2.974570e+01
## [3186] 1.270054e+01 3.557438e+00 1.587331e+01 5.580735e+00 3.875677e+00
## [3191] 3.256217e+01 1.288191e+01 1.400439e+01 2.309481e+01 5.377304e+00
## [3196] 1.393612e+01 1.183241e+01 1.424972e+01 1.323965e+01 8.789002e-01
## [3201] 1.179023e+00 7.565697e+00 4.627072e-01 1.583527e+01 6.648008e+00
## [3206] 3.090043e+01 4.540178e+00 3.551165e+00 8.742145e+00 7.749520e+00
## [3211] 1.966121e+01 1.127422e+01 2.176856e+00 7.842057e-01 1.358292e+01
## [3216] 3.129928e+01 2.910624e+01 3.353870e+00 4.106386e+00 1.164680e+01
## [3221] 1.523459e+01 2.328287e+01 5.751607e+00 7.342954e+00 3.435680e+00
## [3226] 1.060005e+01 7.641312e+00 3.199602e+00 2.054348e+00 1.678668e+00
## [3231] 2.499197e+01 4.246813e+01 2.538575e+00 2.492758e+00 1.737653e+01
## [3236] 8.920853e+00 1.401123e+00 3.686120e+01 4.049372e+00 4.561440e+00
## [3241] 4.864230e+00 1.042034e+01 2.345345e+00 6.341014e+00 4.798742e+00
## [3246] 6.975684e+00 1.713170e+00 2.130224e+01 2.946847e+00 1.839265e+00
## [3251] 1.653198e+01 6.607991e+00 2.040953e+01 5.672877e+01 2.197555e+01
## [3256] 1.036172e+01 5.782613e+00 1.868273e+01 1.069493e+01 1.824656e+01
## [3261] 4.302534e+00 7.809496e+00 2.141083e+01 1.126655e+01 1.118291e+00
## [3266] 3.152528e+00 3.827038e+01 1.408465e+01 3.834588e+00 6.525679e+00
## [3271] 3.659195e+00 1.628028e+00 1.617215e+01 1.101924e+01 8.318776e+01
## [3276] 1.462183e+01 6.879723e+00 7.886562e+00 6.175820e+00 1.033828e+01
## [3281] 9.505528e+00 1.071319e+01 1.385080e+01 2.245727e+01 2.356469e+00
## [3286] 3.994275e+00 4.554757e+00 5.053384e+01 2.180868e+01 4.478506e+00
## [3291] 4.769970e+00 6.501368e+00 8.616560e+00 9.824861e-02 7.921940e+00
## [3296] 3.182926e+01 1.187949e+01 7.611980e+00 1.019221e+01 2.983127e+01
## [3301] 1.381107e+01 1.235514e+01 3.084679e+01 1.493620e+01 2.749181e+01
## [3306] 2.687393e+01 1.792951e+01 1.302730e+00 2.219528e+01 1.798451e+01
## [3311] 1.720690e+01 9.174339e+00 9.353747e+00 4.023284e+00 2.521217e+01
## [3316] 1.187740e+01 1.467922e+01 3.650715e+01 1.689260e+01 5.618926e-01
## [3321] 1.032458e-01 6.430976e-02 2.296819e+01 1.504287e+01 1.067482e+02
## [3326] 4.180723e+00 1.753703e+01 9.825459e+00 3.877416e+00 1.467537e+00
## [3331] 4.689513e+00 9.244401e+00 2.568945e+01 1.876611e+01 6.020986e+00
## [3336] 2.076126e+01 3.692209e+00 3.745365e+00 3.120087e+00 8.066891e-01
## [3341] 5.939738e+00 1.049586e+01 2.868195e+00 1.024782e+01 9.559398e+00
## [3346] 1.321304e+01 1.447321e+01 1.714764e+01 1.536390e+00 2.216768e+00
## [3351] 1.599176e+01 3.399850e+00 3.881028e-01 6.462280e+01 1.808938e+00
## [3356] 1.443610e+00 4.626146e+01 5.025384e+01 1.311644e+00 3.824313e+00
## [3361] 3.971504e+00 2.200463e+01 4.305824e+00 3.834453e+01 5.227934e+00
## [3366] 4.484030e+00 1.414389e+00 1.574926e+01 8.940517e+00 5.024579e+00
## [3371] 3.834169e+00 1.032809e+01 1.647931e+01 7.655748e+00 5.610711e+00
## [3376] 2.492065e+00 9.037266e+00 1.028534e+01 9.792513e+00 1.038710e+01
## [3381] 9.030241e-01 6.537415e+00 5.132691e-01 1.047611e+00 5.112379e-01
## [3386] 3.964122e+00 1.861025e+00 3.122391e+00 4.639597e+00 6.749257e+00
## [3391] 6.369502e+00 2.150440e+00 1.937789e+00 2.348943e+00 3.847488e+01
## [3396] 1.136883e+01 2.133094e+01 4.084016e+00 2.450641e+01 3.916543e+00
## [3401] 1.851776e+01 2.336864e+00 1.035064e+01 6.780931e+00 3.895780e+00
## [3406] 1.049148e+01 1.254893e+00 1.773077e+01 6.866497e+00 8.071699e+00
## [3411] 1.073322e+00 6.146477e+00 2.326106e+00 5.141103e+00 1.858778e+01
## [3416] 1.445223e+00 5.259056e+00 2.426528e+00 1.193203e+01 8.751534e+00
## [3421] 1.624264e+01 6.230805e+00 1.109271e+01 1.547204e+01 6.506111e+00
## [3426] 9.990962e+00 6.689166e+00 1.072433e+01 1.003896e+01 5.618391e-01
## [3431] 1.102532e+01 9.692161e+00 2.319154e+00 3.557387e+00 3.224881e+01
## [3436] 8.043640e-01 3.082767e+01 1.395934e+01 1.851145e+00 5.269956e+00
## [3441] 3.319414e+01 6.392960e+00 1.508240e+00 1.509617e+01 1.294181e+00
## [3446] 2.607627e+01 6.593840e+00 1.525852e+01 1.833167e+01 5.077125e-01
## [3451] 1.406370e+00 2.104638e+00 3.380160e+00 2.335553e+00 7.243899e-01
## [3456] 3.532574e+01 1.014976e+01 2.501642e+01 3.208717e+00 2.812763e+01
## [3461] 2.801059e+01 1.203848e+01 6.096405e+00 1.451805e+01 1.687821e+01
## [3466] 2.094539e+01 2.717741e+01 1.175339e+01 3.027596e+01 9.506186e+00
## [3471] 1.190124e+01 5.520922e+00 9.259792e+00 2.460981e+01 3.910078e+01
## [3476] 1.461009e+00 6.941698e+00 3.430435e+00 3.427924e+00 1.297974e+01
## [3481] 5.788645e+00 2.403116e+00 1.649686e+00 8.270386e+00 1.946347e+00
## [3486] 1.452573e+01 5.078745e+01 8.782257e+00 6.908961e-01 2.248343e+00
## [3491] 4.897923e+01 4.989168e+00 1.301232e+01 9.638875e-01 3.093885e+00
## [3496] 7.428796e+00 5.016392e-01 5.207726e+00 4.299474e+00 7.295965e+00
## [3501] 1.084832e+01 2.288079e+00 5.273018e+01 1.384483e+01 3.052782e+01
## [3506] 1.844215e-01 9.900973e+00 5.109382e+00 1.527506e+01 1.515464e+00
## [3511] 3.277969e+01 9.274076e+00 1.425804e+00 1.438334e+00 2.874474e+01
## [3516] 7.309293e+00 4.308121e+00 1.061078e-01 1.479533e+01 1.826441e+01
## [3521] 2.943968e+01 4.267363e+00 2.575132e+01 2.657421e+00 2.726664e+01
## [3526] 6.913344e+00 1.933357e+00 1.513999e+01 3.851753e+00 6.878595e+00
## [3531] 4.826252e+00 8.584160e+00 3.776289e+01 2.489111e+01 7.097967e+00
## [3536] 5.841287e+00 9.497152e+00 7.698476e+00 1.354847e+01 2.465933e+01
## [3541] 1.825082e+01 2.603379e+00 5.606844e+00 1.106756e+01 1.358909e+01
## [3546] 1.668343e+01 1.469894e+01 2.166126e+00 3.711292e+01 8.089287e-01
## [3551] 7.993054e+00 1.587169e+01 1.447479e+00 2.430934e+00 1.310490e+01
## [3556] 2.184843e+01 1.396264e+00 2.169415e+01 4.055532e+00 9.578593e+00
## [3561] 1.674599e+01 1.879326e+01 2.592344e+00 1.395805e+01 3.010361e+00
## [3566] 5.645761e+00 4.358438e+00 4.141740e+00 5.578953e+00 1.125933e+01
## [3571] 3.457544e+01 1.119176e+01 7.007082e+00 1.763512e+01 6.436372e-01
## [3576] 2.043803e+00 5.205256e+01 2.863627e+00 1.482427e+01 5.025342e+00
## [3581] 4.722181e+00 1.037021e+01 2.082421e+01 1.266765e+01 7.925234e-01
## [3586] 2.365002e+00 1.230033e+00 1.046835e+01 3.655893e-01 1.304403e+01
## [3591] 1.457092e+00 3.119134e+00 2.469496e+00 1.585490e+01 4.181854e+00
## [3596] 1.441064e+00 2.089455e+01 1.538117e+01 5.771518e+00 2.703682e+01
## [3601] 3.918927e+01 1.307479e+01 4.574661e+00 7.307005e+00 8.476989e+00
## [3606] 1.250898e+01 3.448802e+01 8.324039e+00 1.568707e+01 1.037998e+01
## [3611] 2.433375e+00 1.610534e+01 4.806539e+00 3.510320e-01 2.860940e+01
## [3616] 2.082730e+00 7.676609e+00 1.000920e+01 1.022040e+00 3.069291e-01
## [3621] 4.749466e+00 3.114152e+01 3.822620e+01 4.392325e+00 9.366544e+00
## [3626] 5.561473e+00 2.255470e+01 1.345205e+01 1.826810e+01 2.722841e+01
## [3631] 1.220862e+01 1.975229e+00 1.891130e+01 9.760897e-01 1.257811e+01
## [3636] 9.112685e-01 3.953750e+01 1.827952e+01 2.735608e+00 1.914021e+01
## [3641] 1.594030e+01 3.786623e+00 2.520059e+01 1.691046e+01 2.464979e+01
## [3646] 8.568541e+00 4.801324e+00 1.618360e+00 1.838749e+01 3.056764e+00
## [3651] 1.188160e+01 2.177673e-01 8.863854e+00 2.469440e-01 2.734033e+00
## [3656] 4.796231e-01 6.308827e+00 1.683176e+00 2.350200e+01 4.969471e+00
## [3661] 1.419330e+01 1.765339e+01 1.336671e+01 2.542371e+01 5.351386e+00
## [3666] 1.619848e+01 2.403206e+01 1.323677e+01 1.286110e+01 7.669395e+00
## [3671] 2.780901e+01 8.501287e+00 1.112283e+01 1.111933e+01 3.707421e+00
## [3676] 1.876811e+01 3.284278e+01 7.915226e+00 9.473915e-01 5.933140e+00
## [3681] 4.309000e+00 1.698096e+01 8.175558e+00 1.135329e+01 1.007481e+00
## [3686] 4.445199e+00 2.082761e+00 2.736605e+00 9.893459e+00 6.666566e+00
## [3691] 8.849472e-02 4.762083e+01 6.357156e+00 8.019322e-01 1.206868e+01
## [3696] 1.592870e+01 2.121550e+00 8.538980e-01 1.197321e+01 4.570362e+01
## [3701] 2.499605e+01 1.070800e+01 7.271826e+00 2.460397e+01 2.066131e+01
## [3706] 7.391322e-01 1.287861e+01 1.943106e+01 1.975139e+01 2.454200e+01
## [3711] 1.025202e+01 1.420615e+01 2.225721e-01 2.648555e+00 3.878822e+01
## [3716] 5.175290e+00 1.507660e+00 6.938234e+00 8.680821e+00 5.491049e+00
## [3721] 8.309684e+00 2.886009e+01 5.854482e+00 5.430101e+00 2.012537e+01
## [3726] 1.726794e+01 3.863003e+00 1.413433e+01 8.145697e+00 7.782669e-01
## [3731] 5.040589e+00 1.754267e+00 9.404638e+00 1.168472e+01 1.689098e+01
## [3736] 2.568603e+00 6.768095e+00 1.922476e+00 1.907896e+00 1.441652e+01
## [3741] 2.528866e+01 2.080728e+01 1.829370e+01 7.235657e+00 2.773047e+00
## [3746] 8.148580e+00 6.275764e+00 3.666484e+00 2.126488e+01 8.955094e+00
## [3751] 7.877395e+00 9.796958e+00 2.985600e+00 2.462993e+00 4.176016e+00
## [3756] 1.935014e+00 2.333100e+01 3.050807e+00 2.139937e+01 5.196322e+00
## [3761] 1.647210e+01 7.748933e+00 8.257193e+00 1.011190e+01 1.269379e+00
## [3766] 4.582495e-01 1.205322e+01 2.538367e+01 1.783495e+01 9.378352e+00
## [3771] 5.134235e+00 1.293234e+01 1.051238e+01 3.718694e+00 1.756162e+01
## [3776] 1.527304e+00 3.649220e+01 7.090495e+00 2.610987e+00 1.266191e+01
## [3781] 1.975285e+01 8.125325e+00 1.079230e+01 4.077611e+00 2.135320e+01
## [3786] 3.673373e-01 5.009975e+00 5.636019e+00 7.696495e+00 8.108244e+00
## [3791] 4.228329e+01 3.159215e+00 2.659596e+01 9.300041e-01 2.025150e+01
## [3796] 3.461334e+01 1.093079e+01 5.912726e+00 1.012913e+00 4.303772e+00
## [3801] 5.478283e+00 3.815147e+00 2.013036e+01 5.183352e+00 3.934972e+00
## [3806] 3.319885e+01 2.397358e+00 9.469102e+00 1.860859e+00 1.045400e+01
## [3811] 9.829207e+01 3.371535e+01 1.420908e-01 6.041786e+00 1.286599e+01
## [3816] 6.402276e+00 1.579234e+01 6.014593e+00 2.515819e+00 7.397112e-01
## [3821] 4.549272e+00 1.195408e+00 7.451962e+00 3.352595e+01 5.671554e+00
## [3826] 2.575206e+00 2.075389e+01 1.764266e+01 1.543512e+01 2.217171e+01
## [3831] 7.543253e+00 2.618528e-01 1.309140e+01 6.119452e+00 2.446097e+00
## [3836] 2.164122e+00 2.085140e+00 1.887967e+00 2.035326e+01 3.737694e+01
## [3841] 7.613263e+00 3.075185e+01 1.737836e+00 2.581780e+00 3.359109e-02
## [3846] 1.683124e+01 7.281966e+00 8.277066e+00 3.322891e+00 1.409716e+01
## [3851] 9.987156e-01 1.436718e+01 9.061585e-01 9.408072e+00 4.697556e+01
## [3856] 1.150291e+01 2.627361e+01 4.452696e-02 1.965161e+00 5.539098e+00
## [3861] 1.260034e+01 6.033506e+00 6.289967e+00 2.570783e+00 1.486296e+01
## [3866] 2.225921e+01 2.127836e+01 2.072985e+01 9.043024e+00 2.696551e+00
## [3871] 6.021541e+00 1.154561e+00 7.697974e+00 1.633501e+01 4.974637e+00
## [3876] 8.301230e-01 4.452519e+00 1.797492e+01 7.528938e+00 1.110763e+01
## [3881] 2.833654e+01 6.245894e-01 1.100452e+00 1.244412e+01 2.957473e+00
## [3886] 8.855718e+00 2.883135e+01 7.200232e+00 1.203769e+00 3.969887e+01
## [3891] 4.061679e+01 7.126923e+00 8.380953e+00 9.028814e-01 4.801215e+00
## [3896] 3.960073e+00 2.216106e+01 1.702699e+01 1.720626e+01 4.120179e+00
## [3901] 9.570310e+00 1.731916e+01 3.853277e+00 1.178935e+01 8.842181e+00
## [3906] 7.246402e+00 3.634170e+00 1.874969e+01 2.328199e+01 4.275635e+00
## [3911] 1.749553e+00 1.817587e+01 5.740736e+00 2.541706e+01 1.184617e+01
## [3916] 5.997647e-01 1.380509e+01 2.044150e+01 1.863255e+00 1.382394e+00
## [3921] 1.247696e+01 2.838048e+01 1.223570e+01 1.192452e+01 1.105880e+01
## [3926] 8.989282e+00 1.499041e+01 9.387652e+00 1.187094e+01 1.572308e+01
## [3931] 2.867244e+01 3.786654e+01 1.041750e+01 2.320638e+01 1.166092e+01
## [3936] 2.392892e+00 2.925347e+00 6.922149e+00 1.162038e+00 3.459790e+01
## [3941] 2.897735e+01 7.249361e+00 1.115180e+01 2.644155e+01 2.034476e+01
## [3946] 2.273493e+01 2.565372e+01 1.280957e+01 1.238717e+01 1.826959e+00
## [3951] 3.502961e+01 1.171537e+01 7.543875e+00 1.691629e+01 3.920283e+01
## [3956] 1.567616e+01 1.126912e+00 2.150302e+01 2.940207e+00 2.999532e+01
## [3961] 1.628882e+01 1.711858e+00 3.227200e+01 4.907375e+00 2.734924e+00
## [3966] 5.574983e+00 3.589024e+00 2.631881e+00 6.524105e+00 9.393678e+00
## [3971] 2.196256e+00 1.333478e+01 3.193303e+01 2.141091e+00 4.906010e+01
## [3976] 2.323750e+00 4.509131e-01 5.381056e+01 2.964767e+00 3.068361e+00
## [3981] 2.564577e+00 4.915823e+00 3.440343e+01 1.172506e+01 2.575265e+00
## [3986] 3.582941e+01 1.589109e+01 7.767071e+00 8.421399e+00 1.643520e+00
## [3991] 7.675236e+00 5.558481e-01 5.898289e+00 5.902481e+00 2.043202e+01
## [3996] 5.216665e+01 1.606649e+01 8.786195e+00 5.720606e+00 2.506960e+00
## [4001] 3.920138e+00 1.339088e+00 5.156285e+01 3.251661e+01 2.039167e+01
## [4006] 4.723871e+00 1.798392e+01 5.916322e+00 1.175049e+00 1.530478e+01
## [4011] 1.876046e+01 1.445793e+01 5.291139e+01 6.867365e+01 6.724163e+00
## [4016] 1.716263e+00 2.459460e+01 8.771247e+00 1.505625e+01 2.770726e+01
## [4021] 9.835995e+00 3.445813e+00 1.048807e+01 1.009601e+01 9.689267e+00
## [4026] 4.802273e+00 3.968779e+00 1.819992e+00 8.313774e+00 3.190841e+01
## [4031] 1.010745e+01 2.293233e+01 2.512844e+01 2.016800e+01 1.973075e+00
## [4036] 6.790845e+00 8.268085e+00 1.975436e+00 2.100187e+01 1.447007e+01
## [4041] 2.311128e+01 1.581424e+01 3.379851e+00 3.186943e+00 1.047129e+01
## [4046] 4.116567e+01 3.035635e-01 2.905491e+00 3.996406e+00 3.273983e+01
## [4051] 4.188309e+00 6.830785e+01 2.727628e+01 1.038871e+01 1.239346e+01
## [4056] 1.647584e+01 1.182488e+01 1.189557e+01 6.886684e+00 5.339800e+01
## [4061] 3.870773e+00 1.367662e+01 5.673337e-01 4.865856e+00 3.723816e+00
## [4066] 2.613099e+00 1.011350e+01 3.086040e+01 7.945433e+00 1.395602e+00
## [4071] 1.178727e+01 1.789209e+01 1.271326e+01 1.743337e+01 1.563118e+01
## [4076] 6.255547e+00 1.685768e+00 8.117145e+00 4.484831e+01 2.377705e+01
## [4081] 1.054987e+01 5.264360e+00 6.491336e-01 1.764737e+00 2.996398e+00
## [4086] 1.321667e+01 3.955696e+01 4.041969e+00 3.312381e+01 2.756722e+01
## [4091] 1.669149e+01 9.938579e+00 2.252164e+00 7.341303e-01 1.563147e+00
## [4096] 3.752922e+00 2.912391e+00 7.852402e+00 1.468262e+00 8.273321e+00
## [4101] 3.875799e-01 1.093117e+01 8.932902e-01 8.470905e+00 3.036445e+01
## [4106] 7.969575e+00 8.162779e+00 1.293197e+01 1.881630e+00 9.064322e+00
## [4111] 1.471437e+01 7.052196e+00 2.343640e+01 2.490022e+00 6.594377e-01
## [4116] 1.187196e+01 1.369075e+01 1.951076e+01 8.038913e+00 1.976799e+01
## [4121] 1.952850e+01 1.449631e+01 9.099707e+00 9.981735e+00 2.133933e+01
## [4126] 3.879883e+00 1.739341e+00 2.554639e+01 1.502895e+01 2.283197e+00
## [4131] 1.127803e+00 3.061709e+01 2.132192e+01 1.075526e+01 6.245123e+00
## [4136] 6.206263e-01 3.821759e+00 1.293732e+01 2.610903e+01 5.676128e+00
## [4141] 5.035232e+00 5.554579e+00 1.495955e+01 3.332698e+00 1.488420e+01
## [4146] 1.430635e+01 2.797207e+01 1.678352e+01 2.555601e+01 2.075593e+01
## [4151] 1.096527e+01 8.673794e+00 4.966766e+00 1.073463e+01 1.270298e+01
## [4156] 9.555660e+00 5.164754e+00 9.686442e+00 1.980657e+01 1.577506e+01
## [4161] 7.992150e+00 7.673623e+00 5.861032e+00 1.096250e+01 6.651347e+01
## [4166] 6.147648e+00 2.829913e+01 1.190860e+01 6.394784e+00 1.091458e+00
## [4171] 5.556975e+00 1.008800e+00 1.580446e+00 3.993611e+01 5.936839e+00
## [4176] 1.587036e+01 2.319637e+00 2.859818e+00 9.773025e-02 4.430240e+01
## [4181] 6.716301e+00 1.304087e+00 4.188596e+01 3.733653e+00 7.796357e+00
## [4186] 2.732210e-01 2.567076e+01 1.967102e+01 9.209887e+00 3.987120e+00
## [4191] 3.089037e+00 6.065196e-01 4.757161e+00 1.212192e+01 1.805675e+01
## [4196] 1.413958e+01 6.408441e-01 1.720558e+01 1.917709e+01 1.079131e+01
## [4201] 3.769954e+00 2.835634e+01 2.182842e+01 5.521214e+00 1.092069e+01
## [4206] 7.944771e+00 3.905468e+00 9.330888e+00 1.174776e+00 6.080646e+00
## [4211] 5.509122e+00 8.348626e+00 1.717064e+01 8.291612e+00 2.748077e+00
## [4216] 1.019014e+01 1.121049e+01 2.152001e+01 1.078808e-01 4.736471e+00
## [4221] 2.254569e+01 1.361563e+01 2.305096e+01 3.819790e+01 1.752027e+00
## [4226] 1.134081e+00 3.809082e+00 3.521934e+00 3.890919e+00 5.468168e+00
## [4231] 2.002423e+01 1.044154e+01 5.986776e+00 8.284566e+00 1.250155e+00
## [4236] 4.448735e+00 3.877485e+00 3.486557e+00 4.155146e+00 1.358361e+01
## [4241] 6.943467e+00 3.072066e+01 5.578978e-01 7.825269e-01 8.846844e-01
## [4246] 8.792526e-01 5.081997e+00 1.961498e+01 1.307770e+01 6.184333e+00
## [4251] 1.099074e+01 2.502377e+00 1.437281e+01 1.034822e+01 3.541589e+01
## [4256] 7.221280e-01 2.102213e+01 2.112597e+01 2.245388e-01 6.867924e+00
## [4261] 7.524452e+00 1.800028e+01 1.368571e+00 2.388211e-01 1.879611e+01
## [4266] 1.166740e+01 2.744368e+01 1.855967e-01 1.544527e+01 4.653642e-02
## [4271] 2.036176e+00 6.123215e+00 9.437383e+00 1.864313e+01 9.963835e+00
## [4276] 1.410212e+01 8.063109e+00 8.741205e+00 9.851534e-01 6.797189e+00
## [4281] 9.911538e+00 2.101856e+01 4.288170e+00 4.129789e+00 1.380141e+01
## [4286] 2.501233e+00 5.785381e+00 1.495021e+01 4.783466e-02 3.196099e+00
## [4291] 2.946050e+00 4.343547e+01 1.266377e+00 1.125281e+01 8.289341e+00
## [4296] 2.519186e+01 1.899523e+01 7.637322e-01 1.281382e+00 8.544391e+00
## [4301] 3.070720e+00 1.632270e+00 1.543107e+00 2.728046e+01 2.655870e+01
## [4306] 8.096655e+00 1.258378e+01 1.793262e+00 2.575294e+01 1.403202e+01
## [4311] 3.095328e+01 2.585347e+01 3.444326e+00 2.117331e+01 6.993701e-01
## [4316] 1.838563e+00 4.701406e+00 3.991648e+00 1.371688e+00 3.568579e+00
## [4321] 8.356367e-01 1.182392e+01 2.975097e+00 1.687870e+01 7.638255e-01
## [4326] 4.177092e+00 2.832696e+00 2.219463e+00 1.835831e+01 6.809847e+00
## [4331] 5.240634e+01 7.792368e+00 6.033312e+00 4.134184e+00 2.213361e+01
## [4336] 6.414216e+00 1.012723e+01 9.475909e+00 8.434385e+00 1.852560e+00
## [4341] 7.377895e+00 4.035273e-01 2.656502e+00 1.094690e+01 1.678572e+00
## [4346] 1.829010e+00 1.844146e+01 1.602466e+01 2.369171e+01 7.452602e+00
## [4351] 8.892072e+00 3.806229e+01 1.273004e+00 1.473489e+01 2.253612e+01
## [4356] 6.748920e+00 1.156770e+01 9.660101e+00 2.674068e+00 6.451023e+00
## [4361] 8.008840e+00 4.008043e+01 1.625160e+00 6.070522e+00 9.387250e+00
## [4366] 2.218895e+00 2.996549e+00 5.942760e+00 1.402994e+01 1.297765e+01
## [4371] 4.085609e+00 3.097029e+01 1.794462e+00 5.471031e+00 6.244113e+00
## [4376] 1.117999e+01 8.934671e+00 1.588838e+01 1.398362e+00 2.795186e+01
## [4381] 1.054065e+01 7.924312e+00 2.084541e+01 5.695025e+00 7.902938e+00
## [4386] 3.139928e+01 1.960620e+01 5.682551e+00 1.534096e-01 6.212287e+00
## [4391] 3.036401e+00 3.281908e+00 2.560450e+01 6.850249e+00 2.560917e+01
## [4396] 1.022005e+01 3.987110e+01 1.091485e+01 1.061319e+00 1.676154e+01
## [4401] 1.458401e+00 6.587421e+00 2.169751e+00 5.179467e+00 3.301909e+01
## [4406] 6.067697e+00 4.364449e+01 1.003777e+00 2.294307e+01 8.748995e+00
## [4411] 5.019793e+00 1.378579e+01 1.658585e+01 2.627196e+00 2.668551e+01
## [4416] 1.796888e+01 7.094343e+00 7.412215e-01 3.406770e+00 1.459486e+00
## [4421] 5.952305e-01 6.146816e+00 9.541919e-01 4.815270e+00 2.106801e-01
## [4426] 1.721851e+01 1.183197e+01 1.105785e+00 2.965009e+01 2.239151e+00
## [4431] 3.282967e+00 1.424220e+01 2.686800e+00 3.214396e-01 3.477491e+00
## [4436] 9.986826e+00 9.474772e+00 1.477910e+01 6.615407e+00 7.926375e+00
## [4441] 1.691400e+01 2.750408e+00 7.182759e-01 9.759861e+00 3.086252e+00
## [4446] 1.159603e+01 5.110081e+01 2.010318e+01 3.057997e+01 1.606212e+00
## [4451] 1.420969e+01 9.621503e+00 2.920681e-02 3.872431e+00 6.987476e+00
## [4456] 1.283934e+01 4.909937e-01 1.059936e+01 2.479542e+01 5.672886e+00
## [4461] 1.566639e+00 6.189886e+00 4.947734e+00 1.846905e+01 2.061254e+01
## [4466] 5.560888e+00 7.335704e+00 1.402710e+01 7.243376e+00 1.993679e+01
## [4471] 1.136506e+01 6.464032e-01 6.313717e+00 2.800931e+00 7.235080e+00
## [4476] 6.743621e+00 3.498708e+00 5.991773e+00 1.574776e+01 1.043362e+01
## [4481] 1.007042e+01 5.102959e+00 6.534065e+00 1.250815e+01 6.270926e+01
## [4486] 1.597586e+00 2.393187e+01 5.268974e+00 3.186078e+00 1.805042e+00
## [4491] 9.016236e+00 2.037569e+01 1.992764e+01 8.021108e+00 1.041584e+01
## [4496] 6.497566e+00 1.545550e-02 6.566241e+00 9.569092e+00 4.530108e+00
## [4501] 3.552322e+01 5.095950e+00 3.083206e+00 1.817814e+01 9.894812e+00
## [4506] 6.587344e+00 1.017997e+01 1.189714e+01 3.642643e+01 1.393376e+00
## [4511] 1.766815e+01 4.111901e+00 3.545524e+01 1.764363e-01 8.601217e+00
## [4516] 1.588269e+00 3.671106e+00 2.345554e+00 3.727534e+00 3.538802e+00
## [4521] 3.887414e+00 5.133410e+00 3.517377e-01 7.929173e+00 3.751199e+01
## [4526] 1.349138e+01 2.264059e+00 8.986869e+00 5.797157e+00 3.235751e+00
## [4531] 4.131163e+00 2.873095e+01 1.876205e+01 2.008024e+00 1.693264e+01
## [4536] 2.461710e+01 1.647789e+01 9.660196e+00 3.605443e+01 1.526436e+00
## [4541] 1.891023e+01 1.602110e+01 1.144076e+01 1.911311e+01 1.044445e+01
## [4546] 5.302319e+00 2.275387e+00 6.140656e+00 1.554960e+01 1.671467e+01
## [4551] 1.395706e+01 2.169066e+00 4.429565e+00 5.254388e+00 2.262799e+01
## [4556] 1.476819e+01 1.032970e+01 8.747160e+00 7.842642e-01 2.277128e-02
## [4561] 2.754835e+00 6.504917e-01 6.880434e+00 6.445334e+00 6.609723e-01
## [4566] 2.013298e+00 9.668584e+00 1.872374e+01 5.042117e+01 1.477452e+00
## [4571] 1.502601e+01 2.786729e+00 4.180111e-01 2.105872e+00 6.447564e+00
## [4576] 9.456583e+00 2.968840e+00 7.699886e-02 1.040759e+00 2.079316e+01
## [4581] 1.510931e+01 1.764911e+01 2.469036e+00 3.113761e+00 1.895005e+00
## [4586] 2.228350e+01 2.413355e+01 3.590382e+00 1.287105e+01 8.879923e+00
## [4591] 3.430003e+00 6.894042e+00 1.184095e+01 2.015575e+00 5.762500e-01
## [4596] 9.144051e+00 2.644112e+00 1.302023e+01 2.349076e+01 9.232979e+00
## [4601] 4.451909e+01 9.570299e+00 2.057616e+01 4.539424e+01 1.977010e+01
## [4606] 9.177390e+00 2.504187e+00 1.915096e+00 2.169554e+00 3.651714e-01
## [4611] 8.003455e+00 1.579133e+01 3.674447e+00 3.631463e+00 1.003513e+01
## [4616] 3.136483e+01 4.195854e+00 9.099185e-01 2.196152e+01 2.590611e+01
## [4621] 4.236570e+00 8.324801e+00 3.094898e+01 8.931040e+00 1.243944e+01
## [4626] 1.069951e+01 3.648456e+00 5.041090e+00 7.736744e+00 1.009067e+01
## [4631] 1.487992e+01 1.098746e+00 2.251639e+01 9.489084e-01 4.260318e+00
## [4636] 8.080878e+00 2.794983e+00 9.845604e+00 4.339915e+00 6.643636e+00
## [4641] 3.096095e+01 1.700823e+01 1.024663e+01 2.238316e+01 1.269059e+01
## [4646] 2.656841e+00 1.859385e+00 2.485763e-01 3.407384e+00 2.444351e+00
## [4651] 5.068792e-01 1.538339e+01 7.984135e+00 1.199316e+01 9.247534e+00
## [4656] 4.895468e+01 3.505004e+00 3.327761e+00 4.339180e+00 1.700175e+00
## [4661] 7.466687e+00 6.955074e+00 2.619842e+01 6.377992e+00 4.827421e+00
## [4666] 4.455465e+00 2.895362e+01 7.960431e+00 4.892449e+00 7.329771e+00
## [4671] 1.541349e+00 4.811130e+00 1.388565e+01 4.890123e+00 1.784700e+01
## [4676] 2.470496e+01 1.749371e+01 7.399935e+00 1.213252e+00 2.928120e+00
## [4681] 3.730213e+01 1.331731e+00 1.643082e+00 2.787764e-01 2.257932e+01
## [4686] 1.906390e+01 2.553917e+00 3.594111e+00 6.728143e+00 7.476067e+00
## [4691] 5.562535e+00 8.935664e+00 7.221897e+01 2.416996e+00 4.434129e+00
## [4696] 9.274884e+00 3.391591e+01 2.362613e+00 4.200521e+00 5.209014e+01
## [4701] 8.717926e-01 2.100285e+01 2.564065e+01 3.362597e+00 1.257601e+01
## [4706] 1.093051e+01 4.207418e+00 1.319595e+01 7.605680e+00 5.438668e+00
## [4711] 5.819847e+00 1.368094e+01 2.905149e+00 2.214412e+01 3.349132e+00
## [4716] 1.512547e+00 1.523507e+01 2.569450e+01 1.943020e+00 7.802320e+00
## [4721] 4.322628e+00 2.990467e+01 1.316081e+01 3.196126e+00 1.023733e+01
## [4726] 1.542410e+01 4.551895e+00 2.605139e+00 3.843463e+00 9.123554e+00
## [4731] 1.711465e+01 2.487884e+01 1.361809e+01 2.903971e+00 4.489396e+00
## [4736] 1.092033e+00 5.469168e-01 2.790746e+01 1.189175e+00 5.609294e+00
## [4741] 2.962187e+00 8.378815e+00 1.693716e+01 5.804325e+01 2.813989e+01
## [4746] 1.099895e+01 2.102269e+01 5.325101e+00 2.630093e+01 2.116637e+00
## [4751] 2.678272e+00 1.711244e+01 5.890743e+00 1.096828e+00 2.177257e+01
## [4756] 1.063003e+01 1.791865e+01 6.233724e+00 1.732251e+01 2.069679e+00
## [4761] 1.313042e+00 5.313772e+00 8.987548e+00 3.627968e+00 1.086342e+00
## [4766] 6.829394e-01 3.792450e+01 4.909046e+01 2.894870e+00 2.710902e+01
## [4771] 8.008082e+00 4.763532e+00 9.182835e+00 1.815845e+01 1.222871e+01
## [4776] 3.948242e+00 1.585884e+00 4.685044e+00 3.635527e+01 4.119769e+00
## [4781] 1.575067e+01 1.366972e+01 2.429029e+00 1.575517e+00 2.500000e+00
## [4786] 4.366600e+01 6.268536e+00 1.977051e+01 1.438274e+00 2.999730e+00
## [4791] 1.472119e+01 3.012591e+00 2.171487e+00 2.881300e-01 3.264247e+00
## [4796] 6.683249e+00 3.381499e+00 3.963797e+00 9.815629e+00 6.153639e-01
## [4801] 3.499927e+00 6.363640e+00 7.259863e+00 1.018230e+01 1.172299e+00
## [4806] 5.325553e+00 4.249240e+00 3.019385e+01 3.341388e+01 1.656418e+01
## [4811] 5.786495e+00 3.028381e+00 7.858302e+00 6.869277e+01 2.920090e+01
## [4816] 9.822266e+00 9.116246e+00 2.526165e+00 1.337556e+01 5.186201e+00
## [4821] 6.644380e+00 6.263765e+00 1.099492e+00 4.966520e+00 1.024938e+01
## [4826] 2.352088e+01 1.640531e+00 3.432380e+00 8.495378e-01 2.774053e+00
## [4831] 2.754347e+00 1.205339e+01 1.125199e+01 2.526166e+01 1.019716e+01
## [4836] 2.229011e+01 3.678167e+01 5.899137e+00 1.878603e+00 1.211316e+01
## [4841] 6.974017e+00 1.719143e+00 2.027148e+01 4.559997e+00 2.393344e+00
## [4846] 1.978899e+01 1.117482e+01 5.013793e+00 8.225189e-01 8.524802e-01
## [4851] 1.043020e+00 3.636551e+01 7.736684e-01 2.731784e+00 2.517246e+01
## [4856] 1.412007e+01 9.981676e+00 3.694767e+00 2.250448e+01 1.493887e+01
## [4861] 3.167179e+00 5.780697e-03 1.575481e+01 9.990622e+00 5.499803e+00
## [4866] 1.666030e+01 8.086528e+00 1.177979e+01 1.501414e+01 2.023730e+01
## [4871] 1.199392e+01 3.343741e+00 5.297738e+00 9.846821e+00 1.005739e+01
## [4876] 1.751590e+00 1.659261e+01 8.080392e+00 4.664665e+00 1.109204e+00
## [4881] 7.520843e+00 1.699930e+01 3.409467e+01 1.324365e-01 1.714449e+01
## [4886] 1.469139e+00 5.256209e-01 2.820747e+01 2.260986e+00 1.106941e+00
## [4891] 3.362369e+00 6.695056e-01 1.876358e+01 5.329328e+00 1.926400e+01
## [4896] 1.901950e+01 5.352387e+00 9.124394e+00 2.373786e+01 1.481155e-01
## [4901] 1.151113e+01 7.892710e+00 3.978949e+00 1.067255e+01 1.267237e+01
## [4906] 1.522270e+01 2.105588e+01 1.896064e+01 2.300532e+00 9.285203e+00
## [4911] 9.631891e+00 1.395699e+01 2.646875e+00 6.077928e+00 1.741848e+01
## [4916] 1.079491e+00 7.908360e+00 1.047378e+01 3.274359e+00 2.717492e+01
## [4921] 2.776676e+01 5.102216e+00 4.941701e+00 1.838341e+01 4.487525e+00
## [4926] 1.183115e+00 3.997336e-01 4.440527e+00 8.586014e+00 1.038675e+01
## [4931] 9.292818e+00 9.192230e+00 1.775185e+00 6.534448e-03 1.122341e+01
## [4936] 2.252038e+01 6.812610e+00 9.446758e+00 1.645438e+01 8.395682e+01
## [4941] 2.454625e+00 2.340856e+01 3.412533e+01 1.890400e+01 2.733909e+01
## [4946] 7.425579e+00 4.009873e+01 1.224927e+01 3.013637e+00 2.467212e+01
## [4951] 7.787461e+01 1.602551e+01 1.077678e+01 2.295749e+01 4.104361e+00
## [4956] 2.666923e+00 7.455095e+00 7.361184e+00 6.061704e+00 6.419919e+00
## [4961] 3.521705e+00 1.353350e+01 2.321615e-01 3.333489e+00 3.674843e+01
## [4966] 1.343950e+01 3.567743e+00 3.310667e+00 3.973772e+00 2.759451e+01
## [4971] 4.113736e-01 1.458725e+01 2.900068e+01 3.212905e+01 3.722394e+01
## [4976] 1.997431e+00 6.877075e-01 3.244967e+01 3.727701e+01 3.189751e+00
## [4981] 3.334165e+01 2.103436e+01 1.046498e+01 1.027081e+00 4.649067e+00
## [4986] 5.381193e+00 2.798880e-01 3.797807e+00 1.551226e+01 1.041816e+01
## [4991] 1.948316e+01 1.852435e+01 3.800984e+00 1.284673e+01 1.420674e+01
## [4996] 9.328394e+00 2.044910e+01 1.153934e+01 4.541314e+00 1.517504e+01# Histograma
hist(tiempos,breaks=50,col="11",main="Tiempos entre llegadas (Exponencial)",xlab="Minutos")
Interpretación:
La mayoría de intervalos entre llegadas son cortos, ocasionalmente se
presentan intervalos mucho más largos. Esto hace notar un comportamiento
típico de la distribución exponencial.
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.
# Distribución Normal con media = 30, sd = 5
atencion <- rnorm(5000, mean=30, sd=5)
# Histograma con curva normal teórica
hist(atencion, breaks=50, col=14, freq=FALSE,main="Duracion de la atencion",xlab="Minutos")
curve(dnorm(x, mean=30, sd=5), add=TRUE, col="blue", lwd=2)
# Proporción de atenciones > 35 minutos
prop_mas35 <- mean(atencion > 35)
prop_mas35## [1] 0.157Interpretación:
La mayoría de atenciones se concentran alrededor de los 30 minutos, que
es el promedio esperado. La proporción de atenciones que duran más de 35
minutos es 0.157,con esto podemos decir que no son tan
frecuentes las llamadas que duran más de 35 min.
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. a. Simule 1000 horas de operación.
b. b. Cuente cuántos tickets son escalados.
c. c. Grafique usando la función barplot.
# Distribución Binomial: 10 tickets, prob = 0.2
escalados <- rbinom(1000, size=10, prob=0.2)
escalados## [1] 4 4 3 3 1 2 4 0 2 4 2 1 1 2 2 7 1 3 1 3 1 1 2 4 2 2 0 5 2 2 4 2 1 3 0 1 2
## [38] 3 3 2 2 1 2 3 1 3 2 0 0 1 2 3 3 3 1 5 1 4 3 2 1 4 2 2 1 1 1 1 2 1 1 3 2 2
## [75] 3 3 1 1 0 0 2 4 3 1 1 4 3 1 1 1 3 0 0 1 1 2 2 3 2 3 3 2 2 0 1 4 2 2 2 4 5
## [112] 1 0 2 3 3 3 1 1 2 2 1 0 1 1 6 1 1 3 2 3 0 1 2 4 1 1 3 1 4 0 1 4 2 4 2 3 1
## [149] 1 4 1 3 3 0 1 3 2 1 1 1 2 2 0 1 1 1 2 2 0 1 1 2 3 3 1 1 0 3 4 2 3 1 2 1 4
## [186] 2 1 3 3 2 3 2 1 1 3 0 1 4 1 2 2 0 2 1 0 2 0 2 1 4 1 2 0 2 2 1 4 4 3 3 2 1
## [223] 1 0 3 3 3 4 2 0 4 4 2 3 2 1 2 2 1 2 2 2 3 1 2 2 1 0 3 1 2 3 2 2 3 1 3 2 3
## [260] 1 3 3 1 0 1 1 0 1 1 1 3 1 2 5 2 3 2 3 2 1 1 2 3 0 2 1 1 2 1 1 2 0 2 2 1 2
## [297] 0 0 0 3 2 2 3 5 2 3 1 3 3 3 3 5 1 3 2 1 2 2 4 1 2 2 2 4 1 1 2 2 2 1 2 1 0
## [334] 2 1 2 1 1 3 2 2 3 0 2 4 0 3 3 0 2 1 0 4 1 0 1 4 1 1 1 2 2 2 3 0 2 3 1 1 1
## [371] 1 5 3 4 2 4 4 1 2 3 3 3 1 1 3 1 2 1 2 2 1 4 1 2 3 1 4 1 1 2 1 2 3 2 2 2 2
## [408] 4 1 3 2 2 4 3 2 2 2 2 3 1 1 2 3 0 2 0 1 3 5 5 3 2 2 2 2 4 2 1 2 2 3 2 2 2
## [445] 1 5 2 2 3 2 2 4 3 1 3 4 0 2 6 1 1 3 2 2 2 1 3 4 2 2 1 4 1 2 4 4 1 3 1 1 1
## [482] 3 4 2 2 1 1 2 2 4 2 2 1 0 2 2 2 0 2 0 1 1 2 1 1 2 1 5 2 0 2 2 3 3 0 5 1 3
## [519] 2 0 1 1 2 3 5 3 4 1 3 1 2 3 1 0 1 2 0 2 1 3 2 0 3 1 2 1 2 3 3 1 0 2 0 3 3
## [556] 1 4 2 4 3 2 2 2 0 1 4 1 2 2 2 2 1 1 2 1 3 1 0 1 3 1 1 2 2 2 2 4 1 2 1 2 2
## [593] 1 3 5 1 3 1 2 2 7 3 1 3 1 1 1 4 1 2 2 3 1 4 3 1 2 0 1 2 0 1 2 1 2 3 0 1 5
## [630] 2 5 2 3 3 2 0 4 3 2 1 1 2 2 4 0 1 3 3 1 4 4 2 3 2 4 2 3 1 4 4 4 2 3 4 2 4
## [667] 3 1 1 2 2 2 3 3 1 2 2 2 3 1 2 3 3 1 1 3 2 4 3 3 0 4 3 2 3 1 4 2 2 3 3 0 2
## [704] 3 2 1 2 1 2 0 2 1 2 5 1 3 2 4 2 4 1 4 2 2 1 0 1 3 2 4 1 1 5 5 2 1 5 1 2 2
## [741] 3 3 1 1 3 2 2 2 2 3 2 1 1 2 1 2 1 2 2 3 0 1 0 2 1 0 3 1 2 3 2 1 0 2 2 1 1
## [778] 2 0 3 3 3 3 1 0 2 3 1 2 3 1 4 0 3 2 2 4 1 2 3 1 2 3 1 4 0 1 4 1 0 3 2 2 1
## [815] 4 4 2 4 3 1 2 0 3 1 5 3 2 2 1 3 1 2 0 1 5 2 3 2 3 1 4 1 4 2 3 2 2 3 2 2 0
## [852] 0 1 1 1 4 3 1 1 3 4 2 2 2 1 1 5 4 2 3 3 0 1 3 1 2 2 2 5 2 3 3 2 2 2 2 2 4
## [889] 2 0 3 2 4 3 3 3 1 1 2 3 4 4 2 2 1 0 0 3 0 0 2 4 1 4 4 1 2 2 2 0 2 3 1 3 1
## [926] 1 2 1 3 2 2 1 2 4 1 3 1 2 3 2 3 1 1 0 1 4 0 3 6 4 3 1 3 2 1 3 1 2 2 2 3 1
## [963] 2 3 1 3 1 2 2 2 3 3 3 2 2 1 1 2 4 1 2 2 3 3 1 1 2 0 2 3 4 2 0 4 3 2 1 2 2
## [1000] 2# Conteo de tickets escalados
table(escalados)## escalados
## 0 1 2 3 4 5 6 7
## 89 272 316 198 96 24 3 2# Gráfico
barplot(table(escalados),col=12,main="Tickets escalados a segundo nivel",xlab="Tickets escalados",ylab="Frecuencia")
Interpretación: El número de tickets escalados más común es que entre 1 y 3 tickets sean enviados al segundo nivel. Esto concuerda con la probabilidad del 20% de escalamiento.
Conclusiones
En este taller vimos cómo diferentes distribuciones nos
ayudan a entender mejor el sistema de soporte técnico.
1. La distribución Poisson sirvió para simular cuántas
solicitudes llegan por hora, mientras que la Exponencial nos permitió
representar el tiempo que pasa entre cada llegada. Por otro lado, la
Normal describió bien cuánto tardan en promedio los ingenieros en
resolver un ticket, y la Binomial fue útil para calcular los casos en
que un ticket se debe escalar a otro nivel.
2. Al usar estas distribuciones se puede recrear el
funcionamiento del sistema, analizar cómo se comportan las solicitudes y
tener una idea de la capacidad que necesita el equipo para responder de
manera eficiente.