#quick answers
dpois(3,4)[1] 0.19536681-ppois(4,4)[1] 0.3711631qpois(0.5,4)[1] 4sim3.5
Question 1:
lambda_panel <- 5 * 8 * (1 / 10)
lambda_panel[1] 4probA <- dpois(3, lambda = lambda_panel)
probA[1] 0.1953668probB <- 1 - ppois(4, lambda = lambda_panel)
probB[1] 0.3711631medianC <- qpois(0.5, lambda = lambda_panel)
medianC[1] 4set.seed(123)
num_sim <- 10000
sim_flaws <- rpois(num_sim, lambda = lambda_panel)
sim_flaws [1] 3 6 3 6 7 1 4 7 4 4 8 4 5 4 2 7 3 1 3 8 7 5 5 10
[25] 5 5 4 4 3 2 8 7 5 6 1 4 5 2 3 2 2 3 3 3 2 2 2 4
[49] 3 6 1 4 6 2 4 2 2 5 7 3 5 2 3 3 6 4 6 6 6 4 5 5
[73] 5 0 4 2 3 4 3 2 3 5 3 6 2 4 9 7 6 2 2 5 3 5 3 2
[97] 5 2 4 4 4 3 4 8 4 7 7 4 3 2 7 3 1 7 5 2 4 8 4 3
[121] 5 3 3 2 3 9 2 1 2 5 4 7 5 5 4 5 6 6 9 4 3 3 0 2
[145] 6 2 3 1 3 5 6 4 3 3 2 3 4 2 4 2 4 3 5 3 3 4 5 2
[169] 3 3 5 2 6 5 5 4 3 4 6 4 6 3 5 3 4 4 3 4 7 7 3 3
[193] 9 4 7 4 3 5 2 4 3 8 4 4 3 6 3 3 2 2 4 3 2 5 1 5
[217] 3 3 6 7 3 8 5 5 1 3 4 4 5 7 4 3 4 1 3 3 2 6 2 6
[241] 4 5 2 5 3 5 3 8 8 5 3 2 4 3 4 6 2 3 4 6 7 6 5 8
[265] 4 4 3 3 1 4 6 0 1 2 5 5 8 4 1 5 5 2 3 2 1 3 1 2
[289] 1 5 3 2 1 6 5 6 9 2 2 6 5 0 5 5 5 4 2 0 4 4 3 4
[313] 5 1 3 6 6 2 3 6 6 3 2 5 2 1 12 1 3 7 4 3 5 6 3 4
[337] 5 5 5 8 3 2 4 2 4 3 9 3 2 4 2 8 4 2 4 9 5 3 3 6
[361] 2 2 7 3 3 5 2 0 3 4 3 3 6 4 4 8 5 2 3 8 4 5 3 5
[385] 4 7 2 3 2 2 8 3 5 6 2 3 3 2 2 9 9 2 7 4 3 4 5 1
[409] 3 5 3 6 2 4 3 2 8 3 4 1 4 5 4 3 7 4 3 3 2 6 8 4
[433] 3 10 2 4 2 4 2 2 3 4 5 2 6 5 5 2 3 5 4 3 3 1 2 7
[457] 6 5 2 2 8 4 4 2 4 3 2 5 3 6 2 6 3 5 5 4 4 0 2 5
[481] 2 6 3 5 7 2 2 5 3 6 8 1 4 5 1 10 3 1 5 6 3 3 3 1
[505] 3 2 4 4 7 3 4 1 6 3 5 2 4 5 1 6 3 3 3 1 4 5 7 1
[529] 9 3 7 5 4 6 1 5 3 6 4 3 6 2 6 3 5 8 1 6 6 3 3 2
[553] 4 6 4 4 5 4 4 0 1 7 5 2 5 5 3 6 4 6 4 7 4 3 8 5
[577] 3 1 4 4 6 6 6 3 6 2 3 5 8 4 4 1 8 2 1 6 4 3 7 1
[601] 2 5 2 3 2 6 2 6 3 3 5 2 1 10 4 5 7 5 9 1 7 6 5 3
[625] 1 3 3 6 3 3 5 6 4 5 2 2 8 5 6 3 4 6 6 3 1 4 5 1
[649] 3 4 5 7 4 4 5 6 7 1 4 3 6 6 2 5 2 1 7 2 5 2 1 4
[673] 1 3 3 4 6 2 4 4 5 5 6 6 8 4 4 2 4 3 1 5 4 2 3 4
[697] 2 2 3 3 6 3 1 6 3 5 4 3 2 3 5 4 5 5 4 3 0 0 10 2
[721] 3 5 5 6 4 5 6 4 6 1 3 6 5 7 2 3 6 9 3 0 10 2 1 4
[745] 3 4 6 1 5 7 3 3 2 1 4 4 4 6 1 2 4 2 4 4 4 2 2 3
[769] 5 5 7 6 5 6 2 3 3 3 5 6 3 6 0 5 6 4 2 1 3 7 7 4
[793] 2 4 6 3 2 3 3 3 4 3 2 1 3 8 4 4 5 5 1 5 3 6 5 2
[817] 3 2 4 4 5 3 4 9 5 1 4 1 3 5 0 5 4 5 5 4 5 5 3 2
[841] 8 5 4 2 4 3 7 0 2 2 3 5 9 5 4 4 7 2 1 6 3 1 5 4
[865] 4 3 2 2 4 4 2 2 5 4 6 5 0 5 7 5 2 7 5 2 5 7 3 3
[889] 3 2 4 5 5 4 6 5 1 3 1 6 7 4 6 4 5 4 5 7 6 1 0 1
[913] 6 4 3 8 4 4 3 3 6 1 3 6 5 5 3 4 2 5 6 2 5 4 8 2
[937] 4 6 6 1 8 4 3 3 2 2 3 3 3 3 4 2 8 1 3 8 5 1 3 3
[961] 4 4 4 2 7 4 4 2 5 4 5 1 6 3 3 5 7 0 3 3 4 5 7 4
[985] 7 5 2 2 2 3 1 2 4 3 4 6 5 3 5 2 3 4 2 6 6 4 5 3
[1009] 1 4 4 3 2 4 1 5 4 5 4 3 4 6 4 3 6 3 4 4 3 4 2 4
[1033] 4 2 4 4 2 4 3 4 6 5 4 4 3 1 3 0 6 10 5 6 7 4 4 3
[1057] 5 3 3 5 5 2 3 3 1 5 4 2 8 4 6 6 6 6 5 5 3 1 3 3
[1081] 3 2 3 3 5 3 2 1 6 4 6 1 2 2 5 5 10 4 3 2 6 5 2 5
[1105] 6 4 4 7 8 5 1 6 4 3 3 3 3 7 3 4 2 2 5 3 2 1 7 4
[1129] 2 4 4 6 5 4 5 5 3 3 4 3 6 3 1 8 2 3 4 4 3 2 7 4
[1153] 5 7 4 3 1 6 4 2 3 2 4 3 2 1 5 3 2 8 3 3 5 7 2 4
[1177] 5 3 2 5 0 2 5 6 6 2 3 6 5 4 2 4 4 5 1 2 6 2 8 3
[1201] 6 6 4 5 4 9 1 2 6 4 3 11 3 4 1 6 3 6 2 7 3 4 2 6
[1225] 8 1 4 2 6 4 0 3 3 4 3 1 2 5 7 3 1 3 4 4 6 3 4 1
[1249] 2 5 6 4 4 0 2 6 1 3 9 4 3 4 1 2 5 1 4 7 1 8 1 5
[1273] 4 4 6 4 5 4 3 3 2 6 4 5 4 3 5 4 3 4 6 4 2 6 3 3
[1297] 5 5 6 4 1 4 4 6 5 4 1 2 5 2 2 3 6 2 5 2 5 3 4 1
[1321] 6 3 7 3 8 3 4 4 0 5 4 3 4 4 4 2 5 5 6 4 3 4 3 3
[1345] 5 8 3 5 4 4 1 0 2 1 2 4 2 6 3 4 5 2 6 4 2 3 2 4
[1369] 2 2 3 2 3 4 5 6 3 8 1 4 4 3 6 1 6 2 2 6 1 2 10 5
[1393] 4 3 4 6 5 4 1 2 2 2 1 4 3 5 4 7 1 7 5 7 4 2 2 5
[1417] 4 3 5 3 6 4 3 7 4 2 4 9 7 4 6 3 6 6 3 3 5 6 5 4
[1441] 2 4 1 4 5 5 1 4 4 3 4 5 5 2 4 6 2 5 6 2 8 5 6 2
[1465] 1 6 7 2 4 4 5 1 5 3 4 5 4 12 6 6 5 2 6 6 9 1 5 3
[1489] 4 6 0 0 10 5 3 6 9 2 5 4 7 9 4 2 5 4 4 4 3 4 4 8
[1513] 6 2 3 3 1 3 3 2 5 0 5 3 5 0 1 3 5 2 6 5 7 3 3 3
[1537] 3 2 7 4 1 5 3 4 5 3 1 3 4 8 8 1 4 3 3 3 5 3 3 9
[1561] 6 3 6 2 4 2 2 7 2 6 3 1 6 3 1 5 1 4 3 4 5 1 2 2
[1585] 6 4 5 3 3 3 6 6 5 4 3 1 4 2 5 3 5 2 3 6 6 1 6 2
[1609] 4 4 4 5 4 9 9 3 4 3 4 2 0 1 1 5 4 6 4 2 4 7 6 4
[1633] 3 5 6 7 2 3 2 6 2 6 5 7 4 7 6 6 3 2 3 5 3 3 1 4
[1657] 2 6 1 5 6 1 3 5 5 3 7 3 3 3 4 4 1 5 2 5 4 5 4 3
[1681] 2 4 10 3 3 1 4 4 5 8 4 1 3 6 6 6 7 5 4 2 5 1 4 7
[1705] 6 5 2 4 9 4 3 1 1 6 3 7 4 4 7 2 6 3 4 3 1 5 2 5
[1729] 4 2 10 4 1 7 6 4 3 6 8 6 2 8 4 0 2 0 6 5 7 3 8 6
[1753] 6 4 8 4 7 3 4 7 5 0 2 4 3 10 6 3 5 7 5 5 2 4 3 4
[1777] 2 3 5 4 2 3 5 4 2 1 8 3 5 6 3 1 4 6 3 3 5 8 4 4
[1801] 2 6 2 5 4 1 8 4 6 4 3 4 6 5 4 4 4 4 4 0 10 3 2 6
[1825] 4 6 1 6 5 5 6 4 7 2 1 3 5 3 7 5 3 4 3 5 4 0 5 2
[1849] 5 3 7 6 4 1 4 4 10 3 5 7 4 5 1 6 4 2 3 6 4 5 3 6
[1873] 3 3 2 7 3 2 7 3 6 2 3 3 1 5 2 3 3 4 4 9 3 5 8 4
[1897] 3 6 2 4 4 3 2 6 4 4 4 5 5 4 1 4 4 4 4 1 1 5 6 2
[1921] 5 4 9 4 4 3 4 1 4 8 4 4 1 1 1 2 4 6 3 5 4 3 0 5
[1945] 1 6 2 5 6 3 2 5 2 3 4 4 3 5 4 2 9 3 2 2 3 3 3 1
[1969] 7 4 2 6 4 4 5 5 2 3 8 2 5 4 2 2 5 2 3 4 4 3 4 2
[1993] 6 2 1 7 3 5 3 4 2 2 2 4 4 4 4 1 0 2 6 3 4 4 10 2
[2017] 5 3 3 0 11 4 11 2 2 3 5 4 3 5 4 4 4 2 2 5 4 8 8 5
[2041] 4 2 4 5 7 7 6 2 1 4 4 2 8 2 7 2 5 5 5 5 2 6 4 6
[2065] 2 0 3 3 6 7 2 7 4 3 5 5 4 3 8 1 2 5 5 2 4 5 3 9
[2089] 5 3 2 3 2 1 3 5 8 3 4 1 5 3 3 8 5 5 2 2 6 6 5 3
[2113] 2 4 4 2 5 1 5 6 7 5 3 2 6 1 6 4 4 7 2 3 2 2 5 4
[2137] 4 6 8 4 5 2 3 1 2 2 3 3 5 5 3 8 5 2 3 3 4 6 2 3
[2161] 8 2 5 5 4 10 1 9 5 4 2 4 2 3 6 1 3 6 1 6 8 5 0 4
[2185] 5 1 6 5 3 5 5 2 5 7 6 5 5 4 3 2 6 5 6 1 2 4 1 5
[2209] 4 3 3 5 2 2 4 2 2 5 4 3 3 5 6 1 10 1 2 3 6 2 6 6
[2233] 4 5 3 4 7 3 1 8 3 5 1 8 7 6 3 5 3 3 12 9 4 5 3 2
[2257] 4 3 1 9 5 6 4 2 5 1 2 7 2 3 3 3 2 1 7 8 7 4 4 1
[2281] 3 7 3 4 4 2 4 2 4 4 2 7 2 3 6 3 3 6 4 6 4 7 2 4
[2305] 5 2 4 5 7 3 4 0 3 5 4 6 2 5 2 4 5 4 3 5 4 2 4 1
[2329] 3 4 1 2 5 5 5 1 2 7 7 7 5 2 7 7 2 1 4 3 4 4 5 6
[2353] 3 5 4 1 1 2 2 3 4 5 3 7 4 3 3 5 5 4 6 3 2 4 3 3
[2377] 7 4 0 7 3 0 9 3 9 2 4 6 2 5 4 0 3 4 7 10 2 4 5 7
[2401] 5 4 2 7 6 3 2 5 5 4 6 5 2 0 6 2 3 4 4 3 4 6 3 3
[2425] 4 4 2 6 4 5 6 3 0 5 1 4 2 5 1 6 5 3 2 1 0 6 3 1
[2449] 3 4 6 3 2 5 6 9 5 3 5 4 2 4 8 2 4 3 1 2 3 1 1 2
[2473] 3 4 3 4 5 2 6 3 2 3 6 3 7 2 2 4 3 5 5 3 4 7 5 6
[2497] 7 3 5 2 6 5 5 3 5 4 5 6 7 4 2 3 2 2 5 4 4 5 4 3
[2521] 5 5 5 2 3 8 3 1 4 8 6 4 5 4 7 2 4 5 6 7 6 2 5 5
[2545] 5 7 3 8 4 2 4 2 4 3 6 4 4 2 4 2 3 6 4 4 4 6 0 3
[2569] 1 6 4 4 3 4 2 1 1 1 3 5 5 2 8 2 4 4 7 6 4 3 4 6
[2593] 4 2 2 6 4 5 6 3 2 4 3 6 2 2 5 2 5 4 5 3 2 3 4 5
[2617] 2 4 4 7 7 2 3 5 5 4 2 2 3 1 5 5 3 4 1 2 7 4 5 4
[2641] 3 7 1 2 8 6 12 3 4 1 6 6 7 0 3 4 3 5 1 5 2 3 5 2
[2665] 3 5 3 4 4 2 1 2 6 2 1 1 3 6 3 4 3 3 7 7 3 5 2 7
[2689] 1 9 2 3 2 4 5 10 2 6 4 9 4 5 1 5 2 7 6 6 6 3 8 4
[2713] 4 3 1 7 2 3 5 4 8 2 4 7 6 7 5 2 2 2 3 5 7 3 6 4
[2737] 5 5 5 6 3 2 2 0 7 6 1 2 2 4 5 2 2 4 3 4 2 7 5 4
[2761] 5 3 5 3 5 3 5 3 5 4 1 3 4 3 4 6 5 1 2 3 3 5 2 8
[2785] 6 4 7 0 5 7 2 4 5 4 6 3 4 5 3 7 2 4 3 1 5 4 3 7
[2809] 4 7 7 3 5 6 7 2 1 9 3 5 4 3 5 6 2 3 6 2 4 3 4 4
[2833] 5 6 4 3 6 4 5 6 4 3 6 5 4 5 5 3 3 2 7 3 4 1 6 3
[2857] 4 7 3 5 5 2 1 3 5 5 5 7 0 3 5 2 0 2 5 6 3 3 3 8
[2881] 4 5 7 4 3 7 5 1 5 6 2 8 1 2 1 3 5 5 4 1 8 4 5 3
[2905] 6 5 7 3 3 5 5 4 6 3 7 5 5 5 5 5 2 4 5 2 5 2 5 7
[2929] 5 5 3 2 4 2 5 3 4 3 2 4 3 6 2 1 2 7 4 5 1 4 1 4
[2953] 6 2 3 6 1 5 4 1 7 2 5 3 5 2 6 1 2 3 5 3 3 1 4 4
[2977] 9 2 6 1 5 2 2 2 2 7 9 3 2 5 4 3 6 3 6 2 6 1 4 5
[3001] 2 7 3 4 2 5 5 4 6 6 9 5 5 1 2 1 6 3 6 2 3 5 1 3
[3025] 5 6 6 8 3 8 5 3 3 2 5 4 4 1 3 7 4 1 3 2 3 5 3 5
[3049] 4 6 4 2 7 1 1 6 3 5 5 9 8 2 5 1 4 6 3 7 5 3 6 6
[3073] 3 3 4 6 4 5 5 5 6 2 4 3 4 3 7 3 4 1 7 5 4 2 5 4
[3097] 1 1 4 2 4 9 2 5 2 4 6 2 6 3 2 2 5 5 2 9 2 7 5 4
[3121] 3 3 6 7 4 6 5 3 3 8 2 5 6 2 4 2 3 3 4 5 7 3 3 3
[3145] 2 2 3 7 1 4 6 6 4 3 4 2 4 2 3 5 2 3 6 2 1 5 5 4
[3169] 2 2 4 1 2 6 3 0 8 1 5 6 0 6 4 3 3 5 2 3 4 5 4 5
[3193] 3 7 8 5 0 4 6 2 3 4 5 3 3 3 3 4 1 4 3 1 10 4 6 3
[3217] 8 3 6 0 6 1 6 4 5 5 3 5 3 4 1 3 4 4 6 4 6 4 4 4
[3241] 3 4 12 7 5 6 7 4 3 5 4 0 5 3 8 2 3 7 6 4 0 3 3 5
[3265] 2 8 6 3 4 3 3 3 7 3 6 6 2 2 5 4 2 2 3 4 7 3 7 2
[3289] 6 3 3 2 1 2 2 2 6 0 3 7 0 3 3 4 7 4 5 4 2 4 1 5
[3313] 2 6 4 3 6 1 1 4 6 4 4 2 5 4 1 6 3 4 3 2 6 4 6 2
[3337] 5 4 7 4 3 7 6 3 4 5 3 6 6 3 7 1 6 4 3 4 3 5 7 4
[3361] 5 3 6 6 3 4 7 4 2 5 5 5 2 8 0 7 1 6 4 4 6 3 1 2
[3385] 2 2 8 2 3 5 5 3 3 3 3 7 4 4 4 4 3 2 3 3 0 2 8 3
[3409] 8 3 2 4 3 6 7 4 6 3 7 2 2 4 10 4 2 2 5 5 4 5 3 3
[3433] 3 4 2 3 7 9 4 1 4 5 4 4 3 1 2 3 4 2 0 3 1 3 2 3
[3457] 2 4 4 2 7 4 1 2 5 7 6 4 2 2 4 3 6 5 3 5 3 3 4 8
[3481] 4 4 3 3 4 3 8 6 6 5 2 1 2 6 3 5 7 5 4 1 3 3 6 3
[3505] 4 4 2 0 5 6 7 1 5 3 4 2 3 3 5 2 2 4 1 4 4 4 4 5
[3529] 9 6 2 6 4 5 6 3 6 2 4 2 2 7 4 4 8 8 5 5 1 5 7 4
[3553] 5 6 4 6 4 0 4 4 4 4 3 5 4 8 2 8 4 5 6 5 5 10 6 5
[3577] 2 2 4 2 5 4 2 6 7 3 2 5 4 1 4 4 4 3 3 7 5 8 2 4
[3601] 2 4 3 4 4 6 7 4 7 3 4 4 5 2 3 2 4 4 1 5 4 5 3 3
[3625] 5 8 3 2 3 4 3 3 3 5 6 4 4 4 5 5 2 2 7 3 4 8 2 2
[3649] 4 6 6 2 1 5 8 4 4 5 6 4 4 5 3 7 1 3 2 3 4 5 6 3
[3673] 1 7 7 4 7 4 2 2 5 7 2 6 4 1 6 8 6 3 2 2 3 2 2 2
[3697] 5 5 1 1 0 2 7 2 9 5 3 3 5 4 4 3 7 5 5 3 4 8 1 4
[3721] 6 3 3 7 1 4 3 2 4 2 6 5 2 2 3 7 7 2 7 1 6 1 8 2
[3745] 4 5 3 1 5 3 6 4 10 1 1 4 4 0 5 1 4 7 1 8 5 6 2 10
[3769] 5 3 6 8 7 2 1 6 6 1 2 5 2 0 7 1 6 2 3 2 5 4 2 3
[3793] 4 7 4 7 3 6 5 3 7 4 3 4 4 6 8 4 3 2 0 5 5 0 2 4
[3817] 2 3 7 3 10 5 2 4 6 5 4 4 4 2 6 2 4 4 2 8 3 1 5 4
[3841] 0 3 6 2 1 5 4 3 3 7 7 2 4 1 4 2 5 2 2 5 3 4 6 5
[3865] 5 4 2 6 5 6 1 6 3 3 6 2 0 5 1 6 7 2 2 6 7 3 3 3
[3889] 5 3 6 3 3 0 3 4 3 2 11 3 4 2 5 4 3 3 3 6 7 5 3 5
[3913] 4 1 5 4 3 1 8 9 1 4 8 2 3 4 7 4 1 6 6 6 6 0 2 6
[3937] 2 1 4 5 6 1 2 3 3 4 7 9 2 3 6 9 5 1 2 3 3 3 5 2
[3961] 4 5 7 5 3 0 1 2 6 1 3 6 4 6 8 5 3 8 7 4 2 4 6 2
[3985] 4 9 2 3 2 3 4 3 4 9 4 2 5 5 3 3 3 6 4 6 3 2 6 0
[4009] 4 8 3 9 1 3 3 7 9 5 3 3 2 5 5 4 5 5 5 4 3 5 6 4
[4033] 2 4 4 7 3 5 5 5 4 4 6 4 9 1 4 2 3 6 2 4 3 3 4 5
[4057] 8 2 2 4 2 2 3 3 5 5 6 3 2 4 4 4 4 2 6 9 6 6 3 4
[4081] 4 1 5 6 1 7 3 5 5 5 3 3 4 1 4 4 2 8 2 4 3 2 3 11
[4105] 6 3 7 5 4 6 5 3 4 4 5 3 4 4 4 6 6 6 2 3 7 7 5 6
[4129] 4 1 3 4 4 7 5 0 1 3 3 6 5 5 3 2 2 5 3 2 4 2 1 0
[4153] 6 6 0 4 3 4 2 7 2 2 2 3 4 2 4 4 3 9 0 6 2 2 4 5
[4177] 2 2 2 2 6 5 4 6 2 3 3 1 3 5 3 5 2 5 4 1 5 6 4 4
[4201] 3 1 5 4 6 4 4 6 5 1 2 6 3 4 3 4 4 2 5 3 4 3 2 3
[4225] 2 3 4 3 7 3 2 4 3 7 5 4 3 1 4 3 4 6 2 1 6 2 6 1
[4249] 6 6 7 3 3 7 3 7 4 4 5 3 3 3 3 5 3 6 7 4 0 7 3 6
[4273] 4 4 2 1 5 3 1 1 6 5 1 5 0 4 2 4 4 4 3 3 3 2 5 0
[4297] 2 4 4 4 5 14 8 8 5 5 8 2 5 2 4 5 0 2 2 6 3 5 5 3
[4321] 3 3 5 4 2 3 3 4 4 3 3 7 4 4 3 3 5 3 4 2 4 7 1 3
[4345] 3 4 1 5 1 3 3 4 4 10 4 3 6 3 5 7 6 1 3 4 3 6 6 5
[4369] 4 6 1 3 2 6 6 6 3 1 5 5 4 3 3 3 3 4 5 3 4 5 7 7
[4393] 3 5 2 1 4 6 5 4 9 10 3 2 3 4 6 5 7 5 3 3 5 2 3 7
[4417] 2 2 5 4 4 5 5 5 3 9 8 1 5 3 3 1 5 2 2 5 4 1 7 5
[4441] 3 2 6 5 3 2 0 3 2 4 4 3 7 5 3 5 4 3 2 1 2 4 2 1
[4465] 7 6 6 4 5 6 6 5 3 4 5 3 4 3 2 3 2 2 4 7 4 3 3 4
[4489] 2 5 0 0 5 2 3 2 5 4 1 3 2 3 4 4 1 3 1 3 5 5 6 1
[4513] 2 5 3 2 2 2 4 4 4 6 2 5 2 2 2 6 5 4 5 5 5 7 2 4
[4537] 1 2 5 5 3 3 4 1 6 5 2 4 6 2 3 5 2 1 3 2 5 4 3 2
[4561] 2 3 3 1 0 6 3 8 5 6 3 7 5 3 5 7 5 5 5 2 1 3 4 8
[4585] 7 5 3 4 5 6 4 2 5 6 3 2 3 1 4 4 4 7 3 2 4 1 5 5
[4609] 2 2 6 3 9 5 7 5 3 3 1 7 4 3 6 6 5 4 2 6 2 6 4 4
[4633] 5 3 6 6 6 3 2 5 2 1 1 5 5 2 6 6 5 8 2 1 7 6 3 3
[4657] 8 2 5 4 6 5 5 2 4 4 2 6 3 5 4 4 4 2 4 2 3 5 4 3
[4681] 3 0 3 5 1 8 6 7 4 3 4 2 2 3 3 5 2 4 2 4 1 6 6 2
[4705] 4 4 2 5 6 8 5 0 5 3 3 0 3 3 4 6 5 3 6 3 7 5 3 3
[4729] 2 6 4 7 11 4 3 5 6 8 3 5 3 4 3 5 3 5 8 1 4 5 5 6
[4753] 6 6 9 4 5 4 1 4 2 4 1 5 0 1 7 8 3 5 5 4 6 5 3 1
[4777] 4 3 5 5 4 4 2 4 5 3 5 5 3 3 2 4 5 4 7 0 7 4 6 4
[4801] 3 3 3 2 3 3 3 1 5 4 4 2 1 2 1 7 4 6 4 2 0 3 2 6
[4825] 4 4 7 1 1 4 2 3 2 2 4 1 5 5 3 5 1 4 3 2 3 4 3 5
[4849] 7 4 3 5 4 2 3 2 2 5 5 4 2 6 10 1 4 6 4 3 4 3 8 5
[4873] 5 0 3 4 2 3 2 3 2 4 6 4 3 3 2 1 6 8 7 3 3 3 3 4
[4897] 5 2 4 1 5 8 8 7 4 3 3 7 5 3 4 5 5 4 3 3 5 5 1 4
[4921] 4 2 3 2 2 6 3 1 5 5 4 4 5 6 6 4 6 2 3 3 2 0 3 2
[4945] 6 4 4 4 1 5 5 2 4 5 3 5 4 3 7 1 7 6 3 3 4 4 1 3
[4969] 2 2 8 3 7 6 3 6 3 5 1 2 9 1 4 5 3 4 6 4 2 3 5 1
[4993] 7 5 3 2 7 2 5 0 3 9 5 5 3 1 3 4 5 3 3 7 4 8 6 9
[5017] 2 3 7 5 9 8 5 3 5 3 3 6 5 5 3 5 4 2 3 6 5 1 5 7
[5041] 7 2 8 7 3 6 6 4 1 6 3 2 6 9 2 1 5 6 2 4 3 6 4 2
[5065] 3 6 1 3 4 4 5 4 4 6 3 1 6 5 6 1 0 4 6 4 1 3 3 4
[5089] 2 4 3 4 7 4 5 1 5 6 1 1 4 6 5 3 6 3 2 4 6 5 1 1
[5113] 8 1 2 4 5 6 4 3 2 6 6 3 4 4 6 7 4 6 6 3 4 3 6 5
[5137] 3 10 5 2 5 3 6 3 3 1 4 0 3 3 6 2 3 4 8 3 6 2 4 4
[5161] 6 3 4 4 5 1 5 5 5 4 3 3 2 3 1 4 3 2 5 3 3 5 2 2
[5185] 9 8 5 1 8 5 6 2 3 4 3 5 1 7 5 6 7 3 2 2 2 4 6 6
[5209] 1 5 8 3 5 4 1 4 5 6 4 6 0 4 4 6 3 4 2 6 4 3 6 4
[5233] 8 2 0 3 5 4 2 1 6 2 5 4 7 4 1 4 5 4 4 4 6 3 3 6
[5257] 6 4 3 4 3 2 4 1 2 2 3 3 6 3 8 4 6 3 3 2 4 2 4 2
[5281] 2 3 4 5 2 3 2 2 5 4 3 6 4 2 2 8 4 4 5 6 5 6 2 3
[5305] 7 3 7 3 5 4 4 4 4 3 4 3 5 5 4 3 5 6 3 4 6 3 4 4
[5329] 1 3 4 4 5 5 7 5 4 3 1 2 4 4 2 3 2 3 2 3 2 1 6 2
[5353] 2 3 3 5 4 2 6 7 3 5 2 6 3 5 2 6 6 6 0 1 3 3 1 5
[5377] 1 6 4 5 7 4 8 3 3 8 3 6 3 5 5 3 0 3 4 4 3 4 2 3
[5401] 1 4 3 8 1 5 4 0 2 5 4 7 5 4 3 3 2 3 3 7 3 5 1 3
[5425] 2 6 3 3 3 2 5 5 7 4 5 5 7 10 3 3 7 3 5 6 2 6 5 0
[5449] 2 3 6 3 3 7 3 4 3 2 2 4 8 3 6 1 5 3 4 1 5 7 5 2
[5473] 7 2 6 5 3 5 3 4 3 5 3 6 3 4 6 5 0 5 3 8 4 5 2 2
[5497] 7 4 3 4 2 4 2 3 6 5 8 2 4 4 4 4 2 5 7 3 5 7 0 4
[5521] 3 4 3 6 2 6 3 4 2 6 5 4 5 8 6 8 5 4 7 5 3 3 0 4
[5545] 4 1 5 2 3 3 7 5 6 3 5 2 4 7 3 3 3 6 5 4 6 3 3 2
[5569] 2 5 10 6 5 4 2 9 6 8 4 5 6 4 4 5 4 3 4 4 5 8 3 3
[5593] 3 4 3 3 4 3 3 3 4 2 2 1 1 5 8 6 5 5 3 5 3 2 5 6
[5617] 3 5 4 7 3 3 3 2 5 7 4 2 7 3 2 7 4 4 3 3 2 6 6 2
[5641] 4 3 1 5 3 4 2 4 6 0 10 6 3 5 4 1 4 3 10 4 0 1 3 2
[5665] 2 4 3 3 3 4 2 1 8 2 4 7 9 4 6 1 2 2 2 3 4 2 3 1
[5689] 5 6 5 4 5 5 4 2 3 4 2 1 5 4 6 5 4 6 5 3 9 2 8 4
[5713] 3 6 5 4 3 4 5 4 4 4 4 4 2 4 6 1 4 6 3 4 4 5 4 8
[5737] 8 4 2 3 10 3 2 3 4 1 1 3 3 1 5 5 5 1 5 5 3 3 1 4
[5761] 2 6 3 7 5 4 6 3 3 5 4 5 4 5 4 7 7 8 2 3 3 2 4 7
[5785] 1 5 2 3 4 2 5 4 6 2 3 3 7 1 2 5 1 9 1 4 6 3 4 4
[5809] 4 7 3 3 7 2 6 3 2 2 1 2 6 3 5 7 3 5 5 3 1 3 3 4
[5833] 5 3 4 3 2 2 6 4 6 6 2 5 3 4 5 7 6 7 3 0 2 5 5 4
[5857] 1 1 2 10 5 4 1 3 2 5 3 6 3 3 1 4 5 6 2 4 4 5 3 4
[5881] 5 3 4 2 4 7 8 4 5 7 5 8 5 3 5 4 7 7 4 4 4 5 8 4
[5905] 3 6 7 4 3 3 8 4 3 3 2 4 6 1 6 3 5 5 4 4 4 5 9 6
[5929] 1 4 2 3 2 2 6 8 3 3 4 4 8 5 3 4 8 4 1 1 7 6 4 2
[5953] 3 2 3 5 7 6 8 3 1 3 12 4 10 5 3 7 4 6 3 8 4 2 5 2
[5977] 4 5 4 4 7 2 0 3 3 7 4 2 2 1 6 1 3 4 3 6 6 7 6 7
[6001] 4 3 3 4 1 5 3 6 10 2 4 5 6 5 3 7 5 3 4 8 7 2 3 3
[6025] 1 8 6 5 3 3 7 3 4 4 7 4 5 2 3 7 5 6 3 2 8 4 4 2
[6049] 1 2 3 4 1 3 0 2 4 3 5 8 2 8 2 5 3 3 1 2 5 3 5 2
[6073] 1 5 3 3 6 0 3 2 4 8 5 6 5 4 6 4 5 4 1 4 3 4 4 3
[6097] 4 2 0 2 2 2 6 3 4 4 1 5 4 5 4 5 5 5 9 3 1 3 3 3
[6121] 4 5 0 2 4 6 3 3 9 4 0 1 7 4 6 6 5 4 4 4 3 4 6 5
[6145] 2 3 5 1 5 5 6 2 3 6 3 6 4 3 4 1 7 6 5 8 4 5 6 3
[6169] 3 2 6 5 2 6 5 4 1 3 4 8 1 4 3 4 1 6 3 4 2 7 5 3
[6193] 3 5 2 3 6 4 8 5 6 4 1 4 7 1 2 5 4 9 5 5 3 10 4 8
[6217] 4 5 5 6 5 0 1 7 3 5 4 8 5 2 3 5 3 4 1 7 2 3 4 4
[6241] 3 2 5 3 5 5 1 4 4 3 5 7 3 3 4 1 3 2 3 4 2 1 5 3
[6265] 2 4 3 2 2 4 2 4 3 6 3 4 3 3 3 5 1 5 4 3 5 3 2 3
[6289] 1 2 9 2 4 5 4 3 3 4 5 9 4 4 3 2 3 3 3 4 3 3 2 1
[6313] 6 4 4 4 2 4 5 1 5 5 4 6 5 4 2 5 3 2 2 6 2 4 3 4
[6337] 4 8 2 3 3 6 1 1 3 3 6 4 2 1 2 6 3 8 5 3 7 5 10 2
[6361] 6 9 5 5 9 3 3 2 3 3 4 3 1 5 1 2 8 4 3 0 3 6 2 3
[6385] 4 4 5 6 3 2 4 3 6 3 4 2 3 6 4 4 2 3 4 5 2 2 7 2
[6409] 0 3 5 4 3 2 8 5 3 2 5 4 5 5 4 1 5 1 8 8 6 3 4 3
[6433] 8 6 5 6 5 3 7 1 4 3 5 4 3 6 4 6 4 5 3 3 9 10 3 4
[6457] 3 9 7 4 4 3 6 7 3 6 4 4 3 1 2 1 3 5 3 3 6 6 3 5
[6481] 4 2 2 1 4 8 1 5 0 9 8 5 5 4 5 5 0 4 5 1 5 6 4 3
[6505] 6 3 6 5 4 4 8 5 6 3 7 1 3 5 4 2 2 5 5 3 4 3 4 6
[6529] 3 5 3 4 8 4 2 6 3 6 1 1 2 6 3 6 3 3 3 4 2 6 3 5
[6553] 6 6 3 4 2 2 2 2 1 3 1 1 2 2 2 4 2 5 8 5 8 7 10 3
[6577] 5 5 4 5 2 1 2 5 3 3 7 4 5 5 6 4 3 4 1 4 4 2 3 3
[6601] 3 6 9 4 6 8 3 6 1 5 3 3 6 4 5 3 4 7 6 10 3 6 3 1
[6625] 3 4 5 2 3 3 5 4 2 4 2 7 4 7 5 5 3 5 3 3 0 3 5 6
[6649] 2 9 5 6 7 4 3 5 5 6 4 6 5 3 2 4 5 1 7 2 8 2 2 4
[6673] 5 3 3 5 5 5 3 2 3 3 5 4 5 4 4 5 5 2 5 3 4 5 4 5
[6697] 6 4 5 7 6 8 6 2 5 6 4 6 2 4 3 4 2 8 3 6 3 4 3 5
[6721] 2 3 3 6 5 5 4 11 3 3 6 3 1 1 5 6 7 4 3 2 5 2 3 4
[6745] 4 3 6 3 2 1 3 2 5 4 5 2 6 2 7 1 5 1 2 2 4 5 3 4
[6769] 4 3 6 6 4 3 4 5 4 5 5 6 2 6 3 6 7 2 5 4 2 3 2 1
[6793] 2 4 5 5 5 2 3 8 3 2 6 6 3 5 4 2 5 6 3 4 2 1 3 2
[6817] 2 4 5 3 7 3 4 5 6 4 3 4 4 4 4 7 1 3 4 5 5 0 5 3
[6841] 7 4 1 3 5 4 5 3 3 5 5 2 1 4 4 1 0 2 4 5 7 4 7 3
[6865] 0 1 5 8 3 3 4 7 0 2 5 2 3 6 5 3 3 4 2 4 5 3 5 7
[6889] 4 4 5 3 3 2 7 8 3 4 3 2 6 3 6 4 5 1 4 1 7 4 2 4
[6913] 6 1 8 6 4 6 5 11 5 4 6 2 2 1 6 5 1 7 9 6 3 4 3 1
[6937] 4 3 2 0 3 3 4 3 3 1 8 4 1 4 4 4 6 1 2 1 4 2 8 2
[6961] 1 4 2 3 2 3 5 3 2 2 5 3 3 2 4 5 6 7 4 5 1 7 3 3
[6985] 5 1 8 6 2 2 3 2 4 5 2 3 1 2 8 5 7 4 1 6 1 6 3 2
[7009] 5 4 4 6 6 9 3 3 2 9 7 7 3 5 3 1 3 8 4 5 0 4 5 4
[7033] 5 4 5 5 3 5 4 6 1 3 5 1 2 5 7 4 2 5 1 4 4 2 1 1
[7057] 2 3 6 2 8 4 3 4 6 1 1 7 8 3 4 3 2 5 5 4 2 5 4 2
[7081] 4 3 6 6 3 3 3 4 4 4 6 2 8 5 7 4 6 8 1 2 6 4 5 5
[7105] 3 3 3 1 1 4 4 3 4 4 1 3 1 3 4 2 2 3 3 2 6 3 3 5
[7129] 4 2 5 3 2 6 7 7 6 4 7 3 3 5 1 4 5 5 5 8 10 3 8 4
[7153] 3 2 2 2 5 3 8 3 2 2 2 6 8 2 8 3 4 2 1 4 3 3 6 5
[7177] 9 0 4 3 3 3 4 6 4 2 2 2 5 8 7 3 4 5 5 4 4 8 5 3
[7201] 3 2 6 9 4 7 3 5 5 3 6 4 4 2 0 7 8 4 2 6 3 4 7 4
[7225] 1 7 2 3 2 2 2 4 6 1 7 6 5 5 3 2 3 4 3 3 3 3 5 0
[7249] 6 2 3 5 4 6 0 7 4 3 2 4 6 5 6 1 0 2 6 3 3 2 4 6
[7273] 6 4 5 6 2 3 4 2 3 2 7 5 1 4 6 4 7 4 0 5 5 4 3 3
[7297] 4 3 3 3 5 1 6 7 5 2 4 3 3 2 4 5 3 5 4 5 2 6 5 2
[7321] 2 4 1 3 4 2 5 4 6 3 5 7 4 8 5 9 2 6 2 3 2 5 4 6
[7345] 5 6 6 6 7 4 5 2 4 6 3 6 4 2 4 6 3 3 3 3 2 3 2 8
[7369] 7 4 4 3 3 5 1 1 4 2 3 1 4 4 3 5 5 4 4 5 3 5 9 4
[7393] 6 6 4 4 2 4 6 4 2 2 4 3 6 1 3 3 3 5 5 2 4 3 3 4
[7417] 3 1 4 3 5 3 7 6 3 7 7 1 1 5 3 2 1 5 4 3 5 5 1 2
[7441] 4 7 2 4 5 0 1 5 6 10 4 8 2 8 4 2 3 6 3 9 1 5 3 3
[7465] 3 5 1 6 4 2 7 5 5 2 2 7 3 5 3 5 5 4 4 1 2 6 1 8
[7489] 5 3 2 4 5 4 4 3 5 3 6 7 1 5 6 5 5 5 3 3 4 1 5 8
[7513] 5 2 1 4 7 7 1 3 1 8 6 0 1 4 3 6 1 5 1 4 3 6 5 5
[7537] 4 4 3 1 4 6 4 5 4 4 3 1 5 4 2 3 5 5 3 3 3 7 5 2
[7561] 3 3 2 8 2 1 5 2 0 6 3 4 4 2 1 6 4 4 5 2 1 4 2 2
[7585] 8 2 3 4 2 5 2 4 3 4 4 3 3 7 4 4 5 1 5 4 5 3 2 5
[7609] 4 4 5 2 4 2 4 2 4 6 4 5 4 8 2 3 4 5 3 6 7 7 3 4
[7633] 4 6 1 4 3 5 2 2 7 4 4 4 4 4 4 2 3 5 4 5 7 4 5 2
[7657] 5 5 2 3 4 4 4 3 3 5 4 2 8 4 2 2 5 2 2 3 5 1 2 3
[7681] 5 3 2 3 4 4 7 2 3 3 4 1 7 5 9 6 10 3 3 5 2 4 5 2
[7705] 5 4 7 3 4 1 4 4 7 5 4 2 5 3 5 2 4 1 3 2 3 4 1 4
[7729] 7 2 1 3 3 4 3 5 6 3 4 3 6 2 3 5 8 2 5 1 5 7 6 2
[7753] 1 4 4 6 4 5 2 3 4 7 2 3 4 1 1 5 4 5 3 6 6 2 1 3
[7777] 4 10 3 3 6 6 1 4 3 3 5 0 5 2 5 1 4 2 1 5 6 5 4 4
[7801] 1 3 3 5 6 2 5 3 3 3 6 8 3 6 5 2 6 5 5 2 3 3 6 5
[7825] 7 0 2 4 3 3 6 3 2 1 1 4 3 2 6 8 1 4 3 2 6 5 4 4
[7849] 5 6 7 7 6 2 5 5 5 2 2 4 6 6 5 6 5 2 4 3 2 1 4 5
[7873] 7 5 3 5 1 4 8 4 3 3 6 2 5 3 8 9 4 4 3 3 8 4 9 3
[7897] 4 7 4 6 5 1 3 3 5 1 2 4 3 4 6 6 2 2 6 2 5 3 7 1
[7921] 9 6 3 3 5 1 7 3 4 5 3 7 2 7 7 5 10 5 2 5 4 9 1 2
[7945] 4 5 3 3 4 7 11 8 1 1 5 1 8 3 3 4 2 2 4 3 7 3 3 9
[7969] 2 2 4 3 1 3 1 6 6 3 5 2 0 6 5 7 0 1 3 3 4 4 1 4
[7993] 7 3 6 2 3 6 6 3 4 4 5 2 5 6 2 3 1 4 9 6 4 3 5 1
[8017] 2 4 6 2 8 8 7 5 1 3 2 3 4 5 5 7 3 4 2 5 4 4 2 7
[8041] 9 9 1 2 5 2 1 0 3 4 7 2 6 6 1 1 1 4 4 5 2 1 5 0
[8065] 2 4 1 1 3 2 2 3 6 5 3 1 4 2 7 1 8 3 4 2 5 7 7 4
[8089] 3 8 2 3 6 5 1 4 3 3 3 7 3 7 0 3 3 2 7 4 3 8 3 6
[8113] 3 0 2 0 4 4 5 6 7 4 1 3 5 7 4 8 4 4 2 3 4 4 2 3
[8137] 5 2 2 1 4 3 0 5 4 8 6 4 5 5 6 5 1 5 3 4 4 4 5 5
[8161] 3 3 3 2 8 3 6 6 1 3 3 3 2 7 11 5 3 3 6 7 4 4 4 4
[8185] 5 6 4 4 6 4 5 4 1 3 3 3 3 6 3 5 6 4 7 6 2 1 5 1
[8209] 2 4 3 3 4 6 3 3 3 1 2 4 3 2 4 6 5 1 2 1 5 3 2 2
[8233] 3 8 5 2 3 4 2 4 4 5 4 3 6 7 3 2 1 6 3 5 3 2 2 4
[8257] 4 7 10 3 6 3 4 6 5 3 7 4 3 6 5 4 5 3 4 7 4 3 5 6
[8281] 4 5 3 3 3 10 4 3 4 1 3 3 4 4 2 6 2 5 7 3 2 9 4 8
[8305] 2 3 3 1 5 2 2 5 5 3 4 6 3 2 4 2 4 5 2 4 1 3 4 4
[8329] 2 3 4 1 1 1 2 5 4 5 6 10 4 1 2 3 3 4 6 5 5 2 5 4
[8353] 6 2 5 4 6 1 2 2 4 2 3 5 4 6 7 2 5 2 3 4 3 3 2 4
[8377] 4 3 3 3 6 3 3 4 5 4 5 5 3 4 7 5 4 2 3 4 4 4 2 2
[8401] 5 2 2 3 7 4 1 0 2 7 3 4 3 5 7 5 4 4 5 0 5 4 4 4
[8425] 6 1 5 5 5 1 1 3 2 1 0 3 3 6 7 4 2 3 4 7 5 7 4 3
[8449] 3 2 3 5 3 5 4 6 7 2 2 4 4 5 4 2 6 2 3 1 5 4 1 4
[8473] 5 3 4 4 2 1 0 5 3 4 5 3 4 3 3 6 4 3 4 9 2 6 4 2
[8497] 4 2 2 5 4 4 4 5 5 2 5 4 5 4 4 6 4 4 5 3 2 3 5 4
[8521] 3 3 9 4 3 1 0 3 7 6 3 4 5 6 4 4 6 6 2 4 2 3 6 6
[8545] 2 6 1 2 5 4 4 7 9 4 5 5 3 7 3 4 8 1 2 3 5 6 5 2
[8569] 3 3 7 3 2 0 4 6 5 2 9 1 5 2 8 3 2 4 1 1 6 2 1 3
[8593] 1 4 5 6 4 3 6 4 7 6 6 0 5 3 5 6 4 3 8 5 4 3 6 6
[8617] 2 4 4 3 1 4 4 3 1 7 4 7 3 5 6 3 3 3 3 2 1 3 5 3
[8641] 6 5 3 9 7 5 3 3 2 6 4 1 5 2 1 2 1 4 4 1 5 7 0 5
[8665] 1 6 4 4 6 6 3 5 6 6 3 3 4 3 7 5 4 2 4 8 2 4 4 5
[8689] 3 4 1 8 2 3 3 4 4 4 6 3 4 4 4 3 6 6 10 3 4 4 6 4
[8713] 5 2 4 5 1 3 2 4 3 4 2 5 2 5 3 4 6 6 2 3 4 3 3 5
[8737] 6 2 4 6 3 3 3 4 6 2 6 6 4 5 12 5 4 3 11 2 4 3 1 8
[8761] 1 4 2 9 7 4 8 5 5 2 4 6 3 3 3 5 2 2 2 5 3 5 3 0
[8785] 5 2 5 2 7 6 0 5 5 2 3 3 3 5 1 1 4 4 2 4 5 5 2 2
[8809] 12 3 2 5 3 4 2 6 3 6 9 4 3 8 5 4 2 5 7 5 5 2 2 4
[8833] 4 3 3 4 5 4 2 3 5 2 7 2 7 0 4 4 5 4 5 5 6 4 5 3
[8857] 5 3 5 2 4 2 5 10 4 5 6 2 3 0 4 3 4 5 2 4 6 3 2 3
[8881] 7 4 2 5 2 11 6 3 4 3 1 5 7 3 0 6 3 2 1 4 3 1 4 5
[8905] 3 3 3 7 4 2 4 2 2 7 1 4 2 1 1 5 5 2 8 5 2 6 2 4
[8929] 2 5 5 7 4 3 5 2 5 5 4 4 5 4 2 5 4 4 3 5 2 2 2 5
[8953] 6 8 2 4 3 3 6 5 5 7 5 4 5 5 4 3 0 3 3 3 1 7 3 7
[8977] 9 2 4 4 2 5 6 1 5 4 4 3 3 1 4 5 4 3 5 1 4 9 3 6
[9001] 6 6 3 4 7 0 2 3 5 1 7 3 6 4 4 5 5 4 0 1 5 5 4 2
[9025] 5 0 4 1 7 6 3 4 5 2 4 0 5 5 2 5 5 3 3 2 5 1 2 3
[9049] 5 3 11 2 7 2 6 6 3 3 4 5 4 4 1 5 3 3 3 5 4 4 3 6
[9073] 5 4 8 3 6 7 5 3 4 4 4 7 6 4 7 5 3 0 6 2 2 2 2 4
[9097] 7 5 4 1 4 6 6 12 3 6 2 2 4 2 1 3 3 7 4 4 1 3 4 6
[9121] 2 8 6 2 3 4 2 3 4 2 4 6 4 3 4 5 3 2 3 4 5 0 7 2
[9145] 1 6 4 3 6 4 2 2 6 1 3 3 5 5 7 2 6 4 6 7 0 3 2 4
[9169] 5 4 2 4 3 5 7 3 4 5 4 2 3 4 1 5 1 2 3 4 5 5 2 3
[9193] 1 3 7 3 5 7 5 2 6 5 5 4 2 2 7 2 2 2 3 5 5 3 4 6
[9217] 5 4 6 3 2 3 2 2 2 4 5 2 3 4 5 5 6 1 3 3 6 4 3 4
[9241] 5 2 4 5 2 4 6 6 5 5 2 2 4 5 10 3 2 5 4 7 7 3 2 5
[9265] 9 1 3 0 3 1 4 4 6 0 12 0 5 9 5 4 1 4 4 4 0 7 3 3
[9289] 7 5 3 4 4 3 4 2 4 1 4 4 1 1 3 3 3 2 5 4 4 7 2 6
[9313] 6 2 7 0 2 3 4 2 2 3 3 4 5 4 6 9 5 4 3 6 6 2 6 3
[9337] 2 6 4 5 2 1 7 3 4 4 6 4 5 3 4 2 5 7 2 5 1 6 3 4
[9361] 4 6 3 5 3 4 6 3 3 2 6 4 2 6 3 3 2 2 3 6 2 2 5 3
[9385] 6 4 4 6 8 1 1 5 2 2 5 3 5 4 4 4 8 4 8 2 1 5 3 4
[9409] 1 3 2 5 4 7 5 5 2 6 4 5 2 6 4 5 4 3 3 5 2 5 3 2
[9433] 5 4 3 6 3 3 2 4 3 4 4 7 2 2 3 4 2 3 5 3 9 9 3 5
[9457] 5 6 7 5 3 6 3 9 5 4 2 6 3 7 3 7 2 11 5 4 4 4 9 4
[9481] 0 6 5 6 2 4 3 5 2 6 5 1 7 7 5 2 2 4 7 8 4 4 4 3
[9505] 4 3 3 4 4 2 2 4 6 4 5 3 4 5 6 4 2 3 6 3 4 3 5 3
[9529] 3 3 2 3 3 2 6 4 6 4 7 7 4 2 2 5 7 3 1 5 4 1 5 2
[9553] 2 7 1 6 5 4 7 4 2 3 3 4 2 3 7 3 3 8 2 6 2 10 3 6
[9577] 3 3 5 5 4 4 5 7 3 3 5 8 0 2 6 4 4 4 3 3 5 8 2 3
[9601] 3 5 4 1 1 2 4 6 4 2 3 4 2 2 6 3 1 2 1 4 3 4 7 3
[9625] 4 1 4 3 3 1 4 2 5 5 5 3 7 2 2 5 4 1 5 2 6 5 3 1
[9649] 5 5 3 4 3 5 6 6 1 2 4 4 6 1 3 6 5 7 3 7 4 4 4 3
[9673] 4 3 2 6 4 3 2 2 3 5 6 2 3 3 4 5 4 8 3 2 6 2 4 3
[9697] 4 8 2 5 3 5 3 2 5 1 6 5 3 8 0 3 2 3 2 6 6 8 4 0
[9721] 7 4 5 4 1 5 5 5 2 3 4 8 4 1 4 4 3 3 8 1 7 13 2 6
[9745] 4 6 6 4 6 5 2 2 7 2 3 7 4 5 4 4 1 4 4 3 0 5 1 4
[9769] 4 3 5 5 6 3 5 4 3 5 2 4 6 1 7 4 6 4 4 3 4 4 7 5
[9793] 0 6 6 3 3 3 2 2 6 6 2 4 5 2 4 6 4 2 1 5 4 7 3 4
[9817] 3 6 2 3 2 6 2 4 7 2 5 3 4 6 8 2 7 3 6 2 2 5 7 5
[9841] 3 4 3 3 4 1 4 3 3 6 5 2 3 8 3 5 3 3 2 7 4 7 4 3
[9865] 3 5 5 6 1 2 4 4 6 4 6 2 9 8 3 4 2 3 4 5 1 7 6 6
[9889] 2 6 5 0 3 4 0 3 4 2 2 6 6 3 0 2 4 4 2 4 6 8 2 2
[9913] 6 7 3 5 4 2 7 5 3 4 8 5 6 7 7 6 0 6 3 2 1 1 5 5
[9937] 6 2 3 3 3 5 1 8 6 5 7 3 1 6 1 1 6 3 7 2 5 4 4 3
[9961] 3 2 5 2 3 3 9 3 3 6 0 3 5 5 2 7 6 4 1 5 3 4 5 5
[9985] 3 6 1 9 1 3 2 6 7 2 4 4 7 2 4 7sim_probA <- mean(sim_flaws == 3)
sim_probB <- mean(sim_flaws >= 5)
sim_medianC <- median(sim_flaws)
data.frame(
Quantity = c("A: P(X=3)", "B: P(X>=5)", "C: median flaws"),
Theoretical = c(probA, probB, medianC),
Simulated = c(sim_probA, sim_probB, sim_medianC)
) Quantity Theoretical Simulated
1 A: P(X=3) 0.1953668 0.1995
2 B: P(X>=5) 0.3711631 0.3653
3 C: median flaws 4.0000000 4.0000##Question 8:
p_odd_formula <- function(lambda) {
(1 - exp(-2 * lambda)) / 2
}
lambda_val <- 0.8
prob_odd_theoretical <- p_odd_formula(lambda_val)
prob_odd_theoretical[1] 0.3990517set.seed(123)
num_sim <- 10000
sim_Y <- rpois(num_sim, lambda = lambda_val)
sim_Y [1] 0 1 0 2 2 0 1 2 1 1 3 1 1 1 0 2 0 0 0 3 2 1 1 4 1 1 1 1 0 0 3 2 1 1 0 1
[37] 1 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 1 0 1 0 0 1 2 0 1 0 0 0 2 0 2 2 1 0 1 1
[73] 1 0 1 0 0 1 0 0 0 1 0 1 0 0 3 2 2 0 0 1 0 1 0 0 1 0 1 1 1 0 1 3 1 2 2 1
[109] 0 0 2 0 0 2 1 0 1 3 1 0 1 0 0 0 0 3 0 0 0 1 1 2 1 1 1 1 2 1 3 0 0 0 0 0
[145] 2 0 0 0 0 1 2 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 2 1 1 1 0 1 2 1
[181] 2 0 1 0 1 1 0 1 2 2 0 0 3 1 2 1 0 1 0 1 0 3 1 1 0 2 0 0 0 0 1 0 0 1 0 1
[217] 0 0 2 2 0 3 1 1 0 0 1 1 1 2 1 0 1 0 0 0 0 2 0 1 1 1 0 1 0 1 0 3 3 1 0 0
[253] 1 0 1 1 0 0 1 2 2 2 1 2 1 1 0 0 0 1 2 0 0 0 1 1 3 1 0 1 1 0 0 0 0 0 0 0
[289] 0 1 0 0 0 2 1 2 3 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 2 0 0 2 2 0 0 1
[325] 0 0 5 0 0 2 1 0 1 2 0 1 1 1 1 3 0 0 1 0 1 0 3 0 0 1 0 3 1 0 1 3 1 0 0 2
[361] 0 0 2 0 0 1 0 0 0 1 0 0 2 1 1 3 1 0 0 3 1 1 0 1 1 2 0 0 0 0 3 0 1 1 0 0
[397] 0 0 0 4 3 0 2 1 0 1 1 0 0 1 0 2 0 1 0 0 2 0 1 0 1 1 1 0 2 1 0 0 0 2 3 1
[433] 0 4 0 1 0 1 0 0 0 1 1 0 2 1 1 0 0 1 1 0 0 0 0 2 2 1 0 0 3 0 1 0 1 0 0 1
[469] 0 2 0 2 0 1 1 0 1 0 0 1 0 2 0 1 2 0 0 1 0 2 3 0 1 1 0 4 0 0 1 1 0 0 0 0
[505] 0 0 1 1 2 0 1 0 2 0 1 0 1 1 0 2 0 0 0 0 1 1 2 0 3 0 2 1 0 2 0 1 0 2 1 0
[541] 1 0 2 0 1 3 0 2 1 0 0 0 1 2 1 1 1 1 1 0 0 2 1 0 1 1 0 2 1 2 1 2 1 0 2 1
[577] 0 0 1 1 2 2 2 0 2 0 0 1 3 1 1 0 3 0 0 2 1 0 2 0 0 1 0 0 0 1 0 2 0 0 1 0
[613] 0 4 1 1 2 1 3 0 2 2 1 0 0 0 0 2 0 0 1 2 1 1 0 0 3 1 2 0 1 1 2 0 0 1 1 0
[649] 0 1 1 2 1 1 1 2 2 0 1 0 2 1 0 1 0 0 2 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 2 2
[685] 3 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 2 0 0 2 0 1 1 0 0 0 1 1 1 1 1 0 0 0 4 0
[721] 0 1 1 2 1 1 2 1 1 0 0 2 1 2 0 0 1 3 0 0 4 0 0 1 0 1 1 0 1 2 0 0 0 0 1 1
[757] 1 2 0 0 1 0 1 1 1 0 0 0 1 1 2 2 1 1 0 0 0 0 1 1 0 2 0 1 2 1 0 0 0 2 2 1
[793] 0 1 1 0 0 0 0 0 1 0 0 0 0 3 1 1 1 1 0 1 0 2 1 0 0 0 1 1 1 0 1 4 1 0 1 0
[829] 0 1 0 1 1 1 1 1 1 1 0 0 3 1 1 0 1 0 2 0 0 0 0 1 4 1 1 0 2 0 0 2 0 0 1 1
[865] 1 0 0 0 1 1 0 0 1 1 2 1 0 1 2 1 0 2 1 0 1 2 0 0 0 0 1 1 1 1 2 1 0 0 0 1
[901] 2 1 2 1 1 1 1 2 2 0 0 0 2 1 0 3 1 1 0 0 1 0 0 2 1 1 0 1 0 1 2 0 1 1 3 0
[937] 1 2 2 0 3 1 0 0 0 0 0 0 0 0 1 0 3 0 0 3 1 0 0 0 1 1 1 0 2 1 1 0 1 1 1 0
[973] 2 0 0 1 2 0 0 0 1 1 2 1 2 1 0 0 0 0 0 0 1 0 1 2 1 0 1 0 0 1 0 2 2 1 1 0
[1009] 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 2 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 2 1 1 1
[1045] 0 0 0 0 2 4 1 2 2 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 3 1 1 2 2 1 1 1 0 0 0 0
[1081] 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 4 1 0 0 1 1 0 1 2 1 1 2 2 1 0 2 1 0 0 0
[1117] 0 2 0 1 0 0 1 0 0 0 2 1 0 1 1 2 1 1 1 1 0 0 1 0 2 0 0 3 0 0 1 1 0 0 2 1
[1153] 1 2 1 0 0 2 1 0 0 0 1 0 0 0 1 0 0 3 0 0 1 2 0 1 1 0 0 1 0 0 1 2 1 0 0 1
[1189] 1 1 0 1 1 1 0 0 2 0 3 0 2 2 1 1 1 3 0 0 1 1 0 5 0 1 0 2 0 1 0 2 0 1 0 2
[1225] 3 0 1 0 2 1 0 0 0 1 0 0 0 1 2 0 0 0 1 0 1 0 1 0 0 1 2 1 1 0 0 2 0 0 3 1
[1261] 0 1 0 0 1 0 1 2 0 3 0 1 1 1 2 1 1 1 0 0 0 2 1 1 1 0 1 1 0 1 2 1 0 2 0 0
[1297] 1 1 2 1 0 1 1 2 1 1 0 0 1 0 0 0 2 0 1 0 1 0 1 0 1 0 2 0 3 0 1 1 0 1 1 0
[1333] 1 1 0 0 1 1 2 1 0 1 0 0 1 3 0 1 1 1 0 0 0 0 0 1 0 2 0 1 1 0 2 0 0 0 0 1
[1369] 0 0 0 0 0 1 1 2 0 3 0 1 1 0 2 0 2 0 0 2 0 0 4 1 0 0 1 1 1 1 0 0 0 0 0 1
[1405] 0 1 1 2 0 2 1 2 1 0 0 1 1 0 1 0 2 1 0 2 1 0 1 3 2 0 2 0 1 1 0 0 1 2 1 1
[1441] 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 2 0 3 1 2 0 0 2 2 0 1 1 1 0 1 0 1 1
[1477] 1 5 2 2 1 0 2 2 4 0 1 0 1 2 0 0 4 1 0 2 4 0 1 0 2 3 1 0 1 1 1 0 0 1 1 3
[1513] 2 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 2 1 2 0 0 0 0 0 2 1 0 1 0 1 1 0 0 0
[1549] 1 3 3 0 1 0 0 0 1 0 0 3 1 0 2 0 1 0 0 2 0 2 0 0 1 0 0 1 0 0 0 1 1 0 0 0
[1585] 2 1 1 0 0 0 1 2 1 1 0 0 1 0 1 0 1 0 0 2 1 0 2 0 1 1 1 1 1 3 3 0 1 0 0 0
[1621] 0 0 0 1 1 2 1 0 1 2 1 1 0 1 2 2 0 0 0 1 0 2 1 2 1 2 1 2 0 0 0 1 0 0 0 1
[1657] 0 2 0 1 2 0 0 1 1 0 2 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 4 0 0 0 1 1 1 3 1 0
[1693] 0 2 2 2 2 1 1 0 1 0 1 2 2 1 0 1 3 1 0 0 0 2 0 2 1 1 2 0 2 0 1 0 0 1 0 1
[1729] 0 0 4 0 0 2 2 1 0 2 2 2 0 3 1 0 0 0 2 1 2 0 3 2 1 1 3 1 2 0 0 2 1 0 0 1
[1765] 0 4 2 0 1 2 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 3 0 1 2 0 0 1 2 0 0 1 3 1 1
[1801] 0 2 0 1 1 0 2 1 2 1 0 1 1 1 1 1 1 0 1 0 4 0 0 2 1 2 0 2 1 1 2 1 2 0 0 0
[1837] 1 0 2 1 0 1 0 1 1 0 1 0 1 0 2 2 1 0 1 1 4 0 1 2 1 1 0 2 1 0 0 2 1 1 0 2
[1873] 0 0 0 2 0 0 2 0 2 0 0 0 0 1 0 0 0 1 1 3 0 1 3 1 0 2 0 1 0 0 0 2 1 1 1 1
[1909] 1 1 0 1 1 1 1 0 0 1 2 0 1 1 3 1 1 0 1 0 1 3 1 0 0 0 0 0 1 1 0 1 1 0 0 1
[1945] 0 2 0 1 2 0 0 1 0 0 1 1 0 1 1 0 3 0 0 0 0 0 0 0 2 1 0 2 1 1 1 1 0 0 2 0
[1981] 1 1 0 0 1 0 0 1 1 0 1 0 2 0 0 2 0 1 0 0 0 0 0 1 1 1 0 0 0 0 2 0 1 1 4 0
[2017] 1 0 0 0 4 0 4 0 0 0 1 1 0 1 1 1 1 0 0 1 1 2 3 1 0 0 0 1 2 2 2 0 0 1 1 0
[2053] 2 0 2 0 1 1 1 1 0 2 1 2 0 0 0 0 2 2 0 2 1 0 1 1 1 0 3 0 0 1 1 0 1 1 0 3
[2089] 1 0 0 0 0 0 0 1 3 0 1 0 1 0 0 3 1 1 0 0 2 2 1 0 0 1 1 0 1 0 1 2 2 1 0 0
[2125] 2 0 2 1 0 2 0 0 0 0 1 1 1 2 3 1 1 0 0 0 0 0 0 0 1 1 0 3 1 0 0 0 1 2 0 0
[2161] 3 0 1 1 1 4 0 3 1 0 0 0 0 0 2 0 0 2 0 1 3 1 0 1 1 0 2 1 0 1 1 0 1 2 2 1
[2197] 1 1 0 0 2 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 2 0 4 0 0 0 2 0 1 2
[2233] 1 1 0 1 2 0 0 3 0 1 0 3 2 2 0 1 0 0 5 3 1 1 0 0 1 0 0 3 1 2 1 0 1 0 0 2
[2269] 0 0 0 0 0 0 2 3 2 1 0 0 0 2 0 1 1 0 1 0 1 1 0 2 0 0 2 0 0 2 1 2 1 2 0 1
[2305] 1 0 1 1 2 0 1 0 0 1 1 2 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 0 2 2 2
[2341] 1 0 2 2 0 0 1 0 1 1 1 2 0 1 1 0 0 0 0 0 1 1 0 2 1 0 0 1 1 1 2 0 0 1 0 0
[2377] 2 1 0 2 0 0 3 0 3 0 1 1 0 1 1 0 0 1 2 4 0 1 1 2 1 1 0 2 1 0 0 1 1 1 2 1
[2413] 0 0 2 0 0 0 1 0 1 2 0 0 1 1 0 2 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 2 0 0
[2449] 0 1 1 0 0 1 2 3 1 0 1 1 0 1 3 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 2 0 0 0 1 0
[2485] 2 0 0 1 0 1 1 0 1 2 1 2 2 0 1 0 2 1 1 0 1 1 1 1 2 1 0 0 0 0 1 1 1 1 1 0
[2521] 1 1 1 0 0 3 0 0 1 2 2 1 1 1 2 0 1 1 2 2 2 0 1 1 1 2 0 3 1 0 1 0 1 0 2 1
[2557] 1 0 1 0 0 2 0 0 1 2 0 0 0 2 1 1 0 1 0 0 0 0 0 1 1 0 3 0 1 1 2 2 1 0 1 1
[2593] 1 0 0 2 1 1 2 0 0 1 0 2 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 2 2 0 0 1 1 1 0 0
[2629] 0 0 1 1 0 1 0 0 2 1 1 1 0 2 0 0 3 1 5 0 1 0 1 2 2 0 0 1 0 1 0 1 0 0 1 0
[2665] 0 1 0 1 1 0 0 0 1 0 0 0 0 2 0 0 0 0 2 2 0 1 0 2 0 3 0 0 0 1 1 4 0 2 1 3
[2701] 0 1 0 1 0 2 2 2 2 0 3 1 1 0 0 2 0 0 1 1 3 0 1 2 2 2 1 0 0 0 0 1 2 0 2 1
[2737] 1 1 1 2 0 0 0 0 2 1 0 0 0 1 1 0 0 1 0 0 0 2 1 1 1 0 1 0 1 0 1 0 1 1 0 0
[2773] 0 0 1 2 1 0 0 0 0 1 0 3 2 1 2 0 1 2 0 1 1 1 2 0 1 1 0 2 0 1 0 0 1 1 0 2
[2809] 1 2 2 0 1 2 2 0 0 3 0 1 1 0 1 2 0 0 1 0 1 0 1 1 1 2 1 0 2 1 1 2 0 0 2 1
[2845] 1 1 1 0 0 0 2 0 1 0 1 0 1 2 0 1 1 0 0 0 1 1 1 2 0 0 1 0 0 0 1 2 0 0 0 3
[2881] 1 1 2 1 0 2 1 0 1 2 0 2 0 0 0 0 1 1 1 0 3 1 1 0 1 1 2 0 0 1 1 0 1 0 2 1
[2917] 1 1 1 1 0 1 1 0 1 0 1 2 1 1 0 0 1 0 1 0 1 0 0 1 0 2 0 0 0 2 0 1 0 1 0 1
[2953] 2 0 0 2 0 1 1 0 2 0 1 0 1 0 2 0 0 0 1 0 0 0 1 1 3 0 2 0 1 0 0 0 0 2 3 0
[2989] 0 1 1 0 2 0 2 0 2 0 0 1 0 2 0 1 0 1 1 1 2 2 3 1 1 0 0 0 2 0 2 0 0 1 0 0
[3025] 1 2 2 3 0 2 1 0 0 0 1 0 1 0 0 2 1 0 0 0 0 1 0 1 1 1 1 0 2 0 0 2 0 1 1 3
[3061] 3 0 1 0 1 1 0 2 1 0 2 1 0 0 1 2 1 1 1 1 2 0 1 0 1 0 2 0 1 0 2 1 1 0 1 1
[3097] 0 0 1 0 1 3 0 1 0 1 2 0 2 0 0 0 1 1 0 3 0 2 1 1 0 0 2 2 1 2 1 0 0 3 0 1
[3133] 2 0 1 0 0 0 1 1 2 0 0 0 0 0 0 2 0 1 1 2 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1
[3169] 0 0 1 0 0 2 0 0 3 0 1 2 0 2 1 0 0 1 0 0 1 1 1 1 0 2 3 1 0 1 1 0 0 1 1 0
[3205] 0 0 0 1 0 1 0 0 4 1 2 0 3 0 2 0 2 0 2 1 1 1 0 1 0 1 0 0 1 1 2 1 2 1 1 1
[3241] 0 1 5 2 1 2 2 1 0 1 1 0 1 0 3 0 0 2 1 1 0 0 0 1 0 3 2 0 0 0 0 0 2 0 2 2
[3277] 0 0 1 1 0 0 0 1 2 0 2 0 2 0 0 0 0 0 0 0 2 0 0 2 0 0 0 1 2 1 1 1 0 1 0 1
[3313] 0 2 1 0 2 0 0 1 2 1 1 0 1 1 0 2 0 1 0 0 2 1 2 0 1 1 2 1 0 2 2 0 1 1 0 2
[3349] 2 0 2 0 2 1 0 1 0 1 2 1 1 0 1 2 0 1 2 1 0 1 1 1 0 3 0 2 0 2 1 1 2 0 0 0
[3385] 0 0 3 0 0 1 1 0 0 0 0 2 1 1 1 1 0 0 0 0 0 0 3 0 3 0 0 1 0 2 2 1 2 0 2 0
[3421] 0 1 4 1 0 0 1 1 1 1 0 0 0 1 0 0 2 3 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0
[3457] 0 1 1 0 2 1 0 0 1 2 2 0 0 0 1 0 1 1 0 1 0 0 1 3 1 1 0 0 0 0 3 2 2 1 0 0
[3493] 0 2 0 1 2 1 1 0 0 0 2 0 0 1 0 0 1 2 2 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1
[3529] 4 2 0 2 1 1 1 0 2 0 1 0 0 2 1 1 3 3 1 1 0 1 2 0 1 2 1 2 1 0 0 1 1 0 0 1
[3565] 1 3 0 3 1 1 2 1 1 4 2 1 0 0 1 0 1 1 0 2 2 0 0 1 1 0 1 1 1 0 0 2 1 3 0 1
[3601] 0 1 0 1 1 2 2 1 2 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 3 0 0 0 1 0 0 0 1 2 1
[3637] 1 1 1 1 0 0 2 0 1 3 0 0 1 2 1 0 0 1 3 1 0 1 2 1 1 1 0 2 0 0 0 0 1 1 1 0
[3673] 0 2 2 1 2 1 0 0 1 2 0 2 1 0 2 3 1 0 0 0 0 0 0 0 1 1 0 0 0 0 2 0 3 1 0 0
[3709] 1 1 1 0 2 1 1 0 1 3 0 1 2 0 0 2 0 1 0 0 1 0 2 1 0 0 0 2 2 0 2 0 2 0 2 0
[3745] 1 1 0 0 1 0 2 1 4 0 0 1 1 0 1 0 1 2 0 3 1 2 0 4 1 0 2 3 2 0 0 2 2 0 0 1
[3781] 0 0 2 0 2 0 0 0 1 1 0 0 0 2 1 2 0 1 1 0 2 1 0 0 1 2 2 1 0 0 0 1 1 0 0 1
[3817] 0 0 2 0 4 1 0 1 2 1 1 1 1 0 2 0 1 1 0 3 0 0 1 1 0 0 2 0 0 1 1 0 0 2 2 0
[3853] 1 0 1 0 1 0 0 1 0 1 2 1 1 1 0 2 1 2 0 2 0 0 2 0 0 1 0 2 2 0 0 1 2 0 0 0
[3889] 1 0 1 0 0 0 0 1 0 0 4 0 1 0 1 1 0 0 0 2 2 1 0 1 1 0 1 1 0 0 3 4 0 1 3 0
[3925] 0 1 2 1 0 2 2 2 2 0 0 2 0 0 1 1 2 0 0 0 0 1 2 3 0 0 2 4 1 0 0 0 0 0 1 0
[3961] 1 1 2 1 0 0 0 0 2 0 0 2 1 1 3 1 0 3 2 1 0 1 2 0 1 3 0 0 0 0 1 0 1 3 1 0
[3997] 1 1 0 0 0 2 1 1 0 0 2 0 1 3 0 3 0 0 0 2 3 1 0 0 0 1 1 1 1 1 1 1 0 1 2 0
[4033] 0 1 1 2 0 1 1 1 1 1 2 1 3 0 1 0 0 2 0 1 0 0 1 1 3 0 0 1 0 0 0 0 1 1 1 0
[4069] 0 1 1 1 1 0 2 4 2 2 0 1 1 0 1 2 0 2 0 1 1 1 0 0 1 0 1 1 0 3 0 1 0 0 0 5
[4105] 1 0 2 1 1 2 1 0 1 1 1 0 1 1 1 2 2 2 0 0 2 2 1 1 1 0 0 1 0 2 1 0 0 0 0 2
[4141] 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 2 0 0 0 0 1 0 1 1 0 3 0 2 0 0 0 1
[4177] 0 0 0 0 2 1 1 2 0 0 0 0 0 1 0 1 0 1 1 0 1 2 1 1 0 0 1 1 1 1 0 2 1 0 0 2
[4213] 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 2 0 0 1 0 2 1 0 0 0 1 0 1 2 0 0 1 0 1 0
[4249] 2 2 2 0 0 2 0 2 1 1 1 0 0 0 0 1 0 2 2 1 0 2 0 2 1 1 0 0 1 0 0 0 2 1 0 1
[4285] 0 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 6 2 2 1 1 3 0 1 0 1 1 0 0 0 1 0 1 1 0
[4321] 0 0 1 1 0 0 0 1 1 0 0 2 1 1 0 0 1 0 1 0 1 2 0 0 0 1 0 1 0 0 0 0 0 4 1 0
[4357] 2 0 1 2 2 0 0 1 0 2 2 1 1 1 0 0 0 2 2 2 0 0 1 1 1 0 0 0 0 1 1 0 1 1 2 2
[4393] 0 1 0 0 1 2 1 1 3 4 0 0 0 1 2 1 2 1 0 0 1 0 0 2 0 0 1 1 1 1 1 1 0 3 3 0
[4429] 1 0 0 0 1 0 0 1 0 0 2 1 0 0 2 1 0 0 0 0 0 1 1 0 2 1 0 1 1 0 0 0 0 1 0 0
[4465] 2 2 2 1 1 1 2 1 0 1 1 0 1 0 0 0 0 0 1 2 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0
[4501] 0 0 1 1 0 0 0 0 1 1 2 0 0 1 0 0 0 0 1 1 1 2 0 1 0 0 0 2 1 1 1 1 1 2 0 0
[4537] 0 0 1 1 0 0 1 0 2 1 0 1 2 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 2 0 3 1 2 0 2
[4573] 1 0 1 2 1 1 1 0 0 0 1 2 2 1 0 1 1 2 1 0 1 2 0 0 0 0 1 1 1 2 0 0 1 0 1 1
[4609] 0 0 2 0 3 1 2 1 0 0 0 2 1 0 2 1 1 1 0 2 0 2 1 1 1 0 1 2 1 0 0 1 0 0 0 1
[4645] 1 0 1 1 1 3 0 0 2 2 0 0 3 0 1 1 2 1 1 0 1 0 0 2 0 1 1 1 1 0 1 0 0 1 1 0
[4681] 0 0 0 1 0 3 1 2 1 0 1 0 0 0 0 1 0 1 0 1 0 1 2 0 1 1 0 1 2 2 1 0 1 0 0 0
[4717] 0 0 1 2 1 0 1 0 2 1 0 0 0 2 1 2 5 1 0 1 2 3 0 1 0 1 0 1 0 1 2 0 1 1 1 2
[4753] 1 2 3 1 1 1 0 1 0 1 0 1 0 0 2 3 0 1 1 1 2 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1
[4789] 0 0 0 1 1 1 2 0 2 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 2 1 1 1 0 0 0 0 1
[4825] 1 1 2 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 1 2 1 0 1 1 0 0 0 0 1 1 0
[4861] 0 2 4 0 1 1 1 0 1 0 3 1 1 0 0 1 0 0 0 0 0 1 2 1 0 0 0 0 1 3 2 0 0 0 0 1
[4897] 1 0 1 0 1 3 3 2 1 0 0 2 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 2 0 0 1 1 1 1
[4933] 1 2 2 1 1 0 0 0 0 0 0 0 2 1 1 1 0 1 1 0 1 1 0 1 1 0 2 0 2 2 0 0 1 1 0 0
[4969] 0 0 3 0 2 2 0 1 0 1 0 0 3 0 1 1 0 1 2 1 0 0 1 0 2 1 0 0 2 0 1 0 0 3 1 1
[5005] 0 0 0 1 1 0 0 2 1 3 2 3 0 0 2 1 3 3 1 0 1 0 0 2 1 1 0 1 1 0 0 2 1 0 1 2
[5041] 2 0 3 2 0 2 2 0 0 2 0 0 2 4 0 0 1 2 0 1 0 2 1 0 0 2 0 0 1 1 1 1 1 2 0 0
[5077] 2 1 2 0 0 1 2 0 0 0 0 1 0 1 0 1 2 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 2 1 0 0
[5113] 3 0 0 0 1 2 1 0 0 2 2 0 1 1 1 2 1 2 1 0 1 0 2 1 0 4 1 0 1 0 1 0 0 0 1 0
[5149] 0 0 2 0 0 0 3 0 1 0 1 1 2 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0
[5185] 3 3 1 0 3 1 2 0 0 1 0 1 0 2 1 2 2 0 0 0 0 1 2 2 0 1 3 0 1 1 0 0 1 1 1 2
[5221] 0 0 1 1 0 1 0 1 1 0 1 1 3 0 0 0 1 1 0 0 2 0 1 0 2 1 0 1 1 1 1 1 2 0 0 1
[5257] 2 1 0 1 0 0 1 0 0 0 0 0 2 0 2 1 2 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1
[5293] 0 0 0 3 1 1 1 1 1 2 0 0 2 0 2 0 1 1 1 1 1 0 1 0 1 1 1 0 1 2 0 0 2 0 1 1
[5329] 0 0 1 1 1 1 2 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 0 2 2 0 1 0 2
[5365] 0 1 0 2 2 2 0 0 0 0 0 1 0 2 1 1 2 1 2 0 0 3 0 1 0 1 1 0 0 0 1 0 0 1 0 0
[5401] 0 1 0 3 0 1 1 0 0 1 1 2 1 1 0 0 0 0 0 2 0 1 0 0 0 2 0 0 0 0 1 1 2 1 1 1
[5437] 2 4 0 0 2 0 1 2 0 2 1 0 0 0 2 0 0 2 0 1 0 0 0 1 3 0 2 0 1 0 1 0 1 2 1 0
[5473] 2 0 1 1 0 1 0 1 0 1 0 2 0 1 2 1 0 1 0 3 0 1 0 0 2 1 0 1 0 1 0 0 1 1 3 0
[5509] 1 1 1 1 0 1 2 0 1 2 0 1 0 1 0 2 0 2 0 1 0 2 1 1 1 3 1 2 1 1 2 1 0 0 0 1
[5545] 1 0 1 0 0 0 2 1 2 0 1 0 1 2 0 0 0 2 1 0 2 0 0 0 0 1 4 2 1 1 0 3 2 3 1 1
[5581] 1 1 1 1 1 0 1 1 1 3 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 3 1 1 1 0 1 0 0 1 2
[5617] 0 1 1 2 0 0 0 0 1 2 1 0 2 0 0 2 0 0 0 0 0 1 2 0 1 0 0 1 0 1 0 1 2 0 4 1
[5653] 0 1 1 0 1 0 4 0 0 0 0 0 0 1 0 0 0 1 0 0 3 0 1 2 4 1 1 0 0 0 0 0 1 0 0 0
[5689] 1 2 1 1 1 1 0 0 0 0 0 0 1 1 2 1 1 2 1 0 3 0 3 1 0 2 1 1 0 1 1 1 1 1 1 1
[5725] 0 1 2 0 1 2 0 1 1 1 1 3 2 1 0 0 4 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1
[5761] 0 1 0 2 1 0 1 0 0 1 0 1 0 1 1 2 2 3 0 0 0 0 1 2 0 1 0 0 1 0 1 1 2 0 0 0
[5797] 2 0 0 1 0 3 0 1 2 0 1 1 0 2 0 0 2 0 2 0 0 0 0 0 2 0 1 2 0 1 1 0 0 0 0 1
[5833] 1 0 1 0 0 0 2 1 2 2 0 1 0 1 1 2 1 2 0 0 0 1 1 1 0 0 0 4 1 1 0 0 0 1 0 2
[5869] 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 2 2 1 1 2 1 2 1 0 1 1 2 2 1 0 1 1 3 1
[5905] 0 2 2 1 0 0 3 1 0 0 0 1 2 0 2 0 1 1 1 1 1 1 3 2 0 1 0 0 0 0 2 3 0 0 0 0
[5941] 3 1 0 1 3 1 0 0 2 2 1 0 0 0 0 1 2 2 3 0 0 0 5 0 4 1 0 2 1 2 0 3 1 0 1 0
[5977] 1 1 1 1 2 0 0 0 0 2 1 0 0 0 2 0 0 1 0 2 2 2 1 2 0 0 0 1 0 1 0 2 4 0 1 1
[6013] 2 1 0 2 1 0 1 3 2 0 0 0 0 3 2 1 0 0 2 0 1 1 2 1 1 0 0 2 1 1 0 0 3 1 1 0
[6049] 0 0 0 1 0 0 0 0 1 0 1 3 0 3 0 1 0 0 0 0 1 0 1 0 0 1 0 0 2 0 0 0 1 3 1 2
[6085] 1 1 2 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 2 0 1 1 0 1 1 1 0 1 1 1 3 0 0 0 0 0
[6121] 0 1 0 0 1 2 0 0 3 1 0 0 2 1 2 2 1 1 1 1 0 1 2 1 0 0 1 0 1 1 2 0 0 2 0 2
[6157] 1 0 1 0 2 2 1 3 1 1 1 0 0 0 2 1 0 2 1 1 0 0 1 3 0 1 0 1 0 2 0 1 0 2 1 0
[6193] 0 1 0 0 2 1 2 1 2 1 0 1 2 0 0 1 1 3 1 1 0 4 0 3 1 1 1 2 1 0 0 2 0 1 1 3
[6229] 1 0 0 1 0 1 0 2 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 2 0 0 1 0 0 0 0 0 0 0 1 0
[6265] 0 1 0 0 0 1 0 1 0 2 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 3 0 1 1 1 0 0 1 1 3
[6301] 1 1 0 0 0 0 0 1 0 0 0 0 2 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1
[6337] 1 3 0 0 0 2 0 0 0 0 2 1 0 0 0 2 0 3 1 0 2 1 4 0 1 3 1 1 3 0 0 0 0 0 1 0
[6373] 0 1 0 0 3 1 0 0 0 2 0 0 1 1 1 2 0 0 1 0 2 0 1 0 0 2 1 1 0 0 1 1 0 0 2 0
[6409] 0 0 1 1 0 0 3 1 0 0 1 1 1 1 1 0 1 0 3 2 2 0 1 0 3 2 1 1 1 0 2 0 1 0 1 1
[6445] 0 2 1 2 1 1 0 0 3 4 0 1 0 3 2 1 1 0 2 2 0 2 1 1 0 0 0 0 0 1 0 0 1 1 0 1
[6481] 1 0 0 0 1 3 0 1 0 3 3 1 1 0 1 1 0 1 1 0 1 2 1 0 1 0 2 1 1 1 3 1 2 0 2 0
[6517] 0 1 0 0 0 1 1 0 1 0 1 2 0 1 0 1 3 1 0 2 0 2 0 0 0 2 0 2 0 0 0 1 0 1 0 1
[6553] 2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 3 1 3 2 4 0 1 1 0 1 0 0 0 1 0 0 2 1
[6589] 1 1 2 1 0 1 0 1 1 0 0 0 0 1 3 1 1 3 0 2 0 1 0 0 2 1 1 0 1 2 2 4 0 2 0 0
[6625] 0 1 1 0 0 0 1 1 0 1 0 2 1 2 1 1 0 1 0 0 0 0 1 2 0 3 1 2 2 1 0 1 1 2 0 2
[6661] 1 0 0 1 1 0 2 0 3 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1
[6697] 2 0 1 2 1 3 2 0 1 1 0 2 0 1 0 1 0 3 0 2 0 1 0 1 0 0 0 2 1 1 1 4 0 0 2 0
[6733] 0 0 1 2 2 1 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 2 0 1 0 0 0 1 1 0 1
[6769] 1 0 2 2 1 0 1 1 1 1 1 2 0 2 0 2 2 0 1 1 0 0 0 0 0 1 1 1 1 0 0 2 0 0 2 2
[6805] 0 1 1 0 1 2 0 0 0 0 0 0 0 1 1 0 2 0 1 1 1 0 0 1 0 1 0 2 0 0 1 1 1 0 1 0
[6841] 2 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 2 1 2 0 0 0 1 3 0 0 1 2 0 0 1 0
[6877] 0 2 1 0 0 1 0 1 1 0 1 2 1 0 1 0 0 0 2 3 0 1 0 0 2 0 2 1 1 0 1 0 2 0 0 1
[6913] 2 0 3 2 1 2 1 4 1 1 2 0 0 0 2 1 0 2 3 2 0 1 0 0 1 0 0 0 0 0 1 0 0 0 3 1
[6949] 0 1 1 1 2 0 0 0 0 0 3 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 2 1 1 0 2 0 0
[6985] 1 0 3 2 0 0 0 0 1 1 0 0 0 0 3 1 2 1 0 2 0 2 0 0 1 1 0 1 2 3 0 0 0 3 2 2
[7021] 0 1 0 0 0 3 1 1 0 1 1 1 1 1 1 1 0 1 1 2 0 0 1 0 0 1 2 1 0 1 0 1 1 0 0 0
[7057] 0 0 1 0 3 1 0 1 2 0 0 2 3 0 1 0 0 1 1 1 0 1 1 0 1 0 2 2 0 0 0 1 1 1 2 0
[7093] 3 1 2 1 2 3 0 0 2 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 2 0 0 1
[7129] 1 0 1 0 0 2 2 2 2 1 2 0 0 1 0 1 1 1 1 3 4 0 3 1 0 0 0 0 1 0 3 0 0 0 0 2
[7165] 3 0 3 0 1 0 0 0 0 0 2 1 3 0 1 0 0 0 1 2 1 0 0 0 1 3 2 0 1 1 1 1 1 3 1 0
[7201] 0 0 2 3 1 2 0 1 1 0 2 1 1 0 0 2 2 1 0 2 0 1 2 1 0 2 0 0 0 0 0 1 2 0 2 2
[7237] 1 1 0 0 0 1 0 0 0 0 1 0 2 0 0 1 1 2 0 2 1 0 0 1 2 1 2 0 0 0 2 0 0 0 0 2
[7273] 2 1 1 1 0 0 1 0 0 0 2 1 0 1 1 1 2 0 0 1 1 0 0 0 1 0 0 0 1 0 2 2 1 0 1 0
[7309] 0 0 0 1 0 1 1 1 0 2 1 0 0 1 0 0 1 0 1 1 2 0 1 2 1 3 1 3 0 1 0 0 0 1 1 1
[7345] 1 2 2 1 2 1 1 0 0 2 0 2 1 0 1 1 0 0 0 0 0 0 0 3 2 1 1 0 0 1 0 0 1 0 0 0
[7381] 1 1 0 1 1 1 1 1 0 1 4 1 2 2 1 1 0 1 2 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1
[7417] 0 0 1 0 1 0 2 2 0 2 2 0 0 1 0 0 0 1 1 0 1 1 0 0 1 2 0 1 1 0 0 1 1 4 1 2
[7453] 0 3 1 0 0 2 0 3 0 1 0 0 0 1 0 2 1 0 2 1 1 0 0 2 0 1 0 1 1 1 1 0 0 2 0 3
[7489] 1 0 0 1 1 1 1 0 1 0 2 2 0 1 2 1 1 1 0 0 1 0 1 3 1 0 0 1 2 2 0 0 0 3 2 0
[7525] 0 1 0 2 0 1 0 1 0 2 1 1 1 1 0 0 1 2 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 2 1 0
[7561] 0 0 0 3 0 0 1 0 0 2 0 1 1 0 0 2 1 1 1 0 0 1 0 0 3 0 0 1 0 1 0 1 0 1 1 0
[7597] 0 2 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 2 1 1 1 3 0 0 1 1 0 2 2 2 0 1
[7633] 1 2 0 1 0 1 0 0 2 1 0 1 1 1 1 0 0 1 1 1 2 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0
[7669] 3 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 2 0 0 0 1 0 2 1 3 2 4 0 0 1 0 1 1 0
[7705] 1 0 2 0 1 0 1 1 2 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 2 0 0 0 0 1 0 1 2 0 1 0
[7741] 2 0 0 1 3 0 1 0 1 2 2 0 0 1 1 2 1 1 0 0 1 2 0 0 1 0 0 1 1 1 0 1 2 0 0 0
[7777] 1 4 0 0 2 2 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 2 0 1 0 0 0 2 3
[7813] 0 2 1 0 2 1 1 0 0 0 1 1 2 0 0 1 0 0 2 0 0 0 0 1 0 0 2 2 0 1 0 0 2 1 1 1
[7849] 1 2 2 2 2 0 1 1 1 0 0 1 1 2 1 2 1 0 1 0 0 0 1 1 2 1 0 1 0 1 3 1 0 0 2 0
[7885] 1 0 2 3 1 1 0 0 3 1 3 0 1 2 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 2 0
[7921] 3 1 0 0 1 0 2 0 1 1 0 2 0 2 2 1 4 1 0 1 1 3 0 0 1 1 0 0 1 2 4 3 0 0 1 0
[7957] 3 0 0 1 0 0 1 0 2 0 0 3 0 0 1 0 0 0 0 2 2 0 1 0 0 2 1 2 0 0 0 0 1 1 0 1
[7993] 2 0 2 0 0 2 2 0 1 1 1 0 1 2 0 0 0 1 3 2 1 0 1 0 0 1 2 0 3 2 2 1 0 0 0 0
[8029] 1 1 1 2 0 1 0 1 1 1 0 2 3 3 0 0 1 0 0 0 0 1 2 0 2 2 0 0 0 1 1 1 0 0 1 0
[8065] 0 1 0 0 0 0 0 0 2 1 0 0 1 0 2 0 3 0 1 0 1 2 2 1 0 3 0 0 2 1 0 0 0 0 0 2
[8101] 0 2 0 0 0 0 2 1 0 3 0 2 0 0 0 0 1 1 1 2 2 0 0 0 1 2 0 3 1 1 0 0 1 1 0 0
[8137] 1 0 0 0 1 0 0 1 1 3 2 1 1 1 2 1 0 1 0 1 1 1 1 1 0 0 0 0 3 0 2 2 0 0 0 0
[8173] 0 2 4 1 0 0 2 2 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 2 0 1 2 1 2 2 0 0 1 0
[8209] 0 0 0 0 1 2 0 0 0 0 0 1 0 0 1 2 1 0 0 0 1 0 0 0 0 3 1 0 0 0 0 1 1 1 1 0
[8245] 2 2 0 0 0 1 0 1 0 0 0 1 1 2 4 0 1 0 0 2 1 0 2 0 0 1 1 1 1 0 1 2 1 0 1 1
[8281] 1 1 0 0 0 4 1 0 1 0 0 0 1 1 0 2 0 1 2 0 0 3 1 3 0 0 0 0 1 0 0 1 1 0 1 1
[8317] 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 2 4 1 0 0 0 0 1 2 1 1 0 1 1
[8353] 2 0 1 1 2 0 0 0 1 0 0 1 1 2 2 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1
[8389] 0 1 2 1 1 0 0 1 1 1 0 0 1 0 0 0 2 1 0 0 0 2 0 1 0 1 2 1 1 1 1 0 1 1 1 1
[8425] 2 0 1 1 1 0 0 0 0 0 0 0 0 2 2 1 0 0 1 2 1 2 1 0 0 0 0 1 0 1 1 2 2 0 0 1
[8461] 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 3 0 2 1 0
[8497] 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 2 1 1 1 0 0 0 1 1 0 0 3 1 0 0 0 0 2 2 0 1
[8533] 1 2 1 1 2 2 0 1 0 0 2 1 0 2 0 0 1 1 1 2 3 1 1 1 0 2 0 1 3 0 0 0 1 1 1 0
[8569] 0 0 2 0 0 0 1 1 1 0 3 0 1 0 3 0 0 1 0 0 2 0 0 0 0 1 1 2 1 0 1 1 2 2 2 0
[8605] 1 0 1 1 1 0 3 1 1 0 1 1 0 1 1 0 0 1 1 0 0 2 0 2 0 1 2 0 0 0 0 0 0 0 1 0
[8641] 2 1 0 3 2 1 0 0 0 2 1 0 1 0 0 0 0 1 1 0 1 2 0 1 0 2 1 1 2 2 0 1 2 2 0 0
[8677] 0 0 2 1 1 0 1 3 0 1 1 1 0 1 0 3 0 0 0 1 1 1 2 0 1 1 0 0 2 2 4 0 1 1 2 1
[8713] 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 2 1 0 0 1 0 0 1 1 0 1 2 0 0 0 1 2 0 2 2
[8749] 1 1 5 1 1 0 4 0 0 0 0 3 0 1 0 3 2 1 3 1 1 0 1 2 0 0 0 1 0 0 0 1 0 1 0 0
[8785] 1 0 1 0 2 2 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 5 0 0 1 0 1 0 1 0 2 3 1
[8821] 0 3 1 1 0 1 2 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 2 0 2 0 1 1 1 0 1 1 2 1 1 0
[8857] 1 0 1 0 1 0 1 4 1 1 2 0 0 0 1 0 1 1 0 1 2 0 0 0 2 1 0 1 0 4 1 0 1 0 0 1
[8893] 2 0 0 2 0 0 0 1 0 0 1 1 0 0 0 2 0 0 1 0 0 2 0 1 0 0 0 1 1 0 3 1 0 2 0 1
[8929] 0 1 1 2 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 2 3 0 1 0 0 2 1 1 2 1 1
[8965] 1 1 0 0 0 0 0 0 0 2 0 2 3 0 1 1 0 1 2 0 1 1 1 0 0 0 0 1 1 0 1 0 1 3 0 1
[9001] 1 2 0 1 2 0 0 0 1 0 2 0 2 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 2 1 0 1 1 0 1 0
[9037] 1 1 0 1 1 0 0 0 1 0 0 0 1 0 5 0 2 0 2 2 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 2
[9073] 1 1 3 0 2 2 1 0 1 1 1 2 2 1 2 1 0 0 2 0 0 0 0 1 2 1 1 0 1 1 2 5 0 2 0 0
[9109] 1 0 0 0 0 2 0 1 0 0 1 2 0 3 2 0 0 1 0 0 1 0 1 2 1 0 1 1 0 0 0 1 1 0 2 0
[9145] 0 2 0 0 2 1 0 0 2 0 0 0 1 1 2 0 2 1 2 2 0 0 0 1 1 1 0 1 0 1 2 0 1 1 1 0
[9181] 0 1 0 1 0 0 0 1 1 1 0 0 0 0 2 0 1 2 1 0 2 1 1 1 0 0 2 0 0 0 0 1 1 0 1 2
[9217] 1 1 2 0 0 0 0 0 0 1 1 0 0 1 1 1 2 0 0 0 2 1 0 1 1 0 1 1 0 1 2 2 1 1 0 0
[9253] 1 1 4 0 0 1 0 2 2 0 0 1 4 0 0 0 0 0 1 1 2 0 5 0 1 3 1 1 0 1 1 1 0 2 0 0
[9289] 2 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 2 0 2 1 0 2 0 0 0 1 0 0 0 0 1
[9325] 1 1 1 3 1 1 0 2 2 0 2 0 0 1 1 1 0 0 2 0 1 1 2 0 1 0 1 0 1 2 0 1 0 2 0 1
[9361] 1 2 0 1 0 1 2 0 0 0 2 1 0 2 0 0 0 0 0 1 0 0 1 0 2 1 1 2 3 0 0 1 0 0 1 0
[9397] 1 1 1 1 3 0 3 0 0 1 0 1 0 0 0 1 1 2 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0
[9433] 1 1 0 2 0 0 0 1 0 0 1 2 0 0 0 1 0 0 1 0 3 3 0 1 1 2 2 1 0 2 0 3 1 1 0 2
[9469] 0 2 0 2 0 4 1 1 0 1 3 1 0 2 1 2 0 1 0 1 0 2 1 0 2 2 1 0 0 1 2 3 0 1 1 0
[9505] 1 0 0 1 1 0 0 1 2 1 1 0 1 1 2 1 0 0 2 0 1 0 1 0 0 0 0 0 0 0 2 1 2 1 2 2
[9541] 1 0 0 1 2 0 0 1 0 0 1 0 0 2 0 2 1 1 2 1 0 0 0 1 0 0 2 0 0 3 0 1 0 4 0 2
[9577] 0 0 1 1 1 1 1 2 0 0 1 3 0 0 2 0 1 1 0 0 1 3 0 0 0 1 1 0 0 0 1 1 1 0 0 1
[9613] 0 0 2 0 0 0 0 1 0 1 2 0 1 0 1 0 0 0 1 0 1 1 1 0 2 0 0 1 0 0 1 0 1 1 0 0
[9649] 1 1 0 1 0 1 2 2 0 0 1 0 2 0 0 2 1 2 0 2 1 1 1 0 1 0 0 2 0 0 0 0 0 1 2 0
[9685] 0 0 1 1 1 3 0 0 1 0 1 0 1 3 0 1 0 1 0 0 1 0 2 1 0 3 0 0 0 0 0 2 2 3 1 0
[9721] 2 1 1 1 0 1 1 1 0 0 1 3 1 0 0 1 0 0 3 0 2 5 0 2 1 2 2 1 2 1 0 0 2 0 0 2
[9757] 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 2 0 1 1 0 1 0 1 1 0 2 1 1 1 1 0 1 1 2 1
[9793] 0 2 2 0 0 0 0 0 1 2 0 1 1 0 1 1 1 0 0 1 1 2 0 1 0 2 0 0 0 2 0 1 2 0 1 0
[9829] 1 2 3 0 2 0 2 0 0 1 2 1 0 1 0 0 1 0 1 0 0 2 1 0 0 3 0 1 0 0 0 2 1 2 1 0
[9865] 0 1 1 2 0 0 1 1 2 1 2 0 3 3 0 1 0 0 1 1 0 2 2 1 0 2 1 0 0 1 0 0 1 0 0 2
[9901] 2 0 0 0 0 1 0 1 2 2 0 0 2 2 0 1 1 0 2 1 0 0 3 1 2 2 2 2 0 2 0 0 0 0 1 1
[9937] 2 0 0 0 0 1 0 3 1 1 2 0 0 2 0 0 2 0 2 0 1 1 1 0 0 0 1 0 0 0 3 0 0 1 0 0
[9973] 1 1 0 2 1 0 0 1 0 1 1 1 0 2 0 3 0 0 0 2 2 0 1 1 2 0 1 2sim_prob_odd <- mean(sim_Y %% 2 == 1) # TRUE when Y is odd
data.frame(
Quantity = "P(Y is odd), lambda = 0.8",
Theoretical = prob_odd_theoretical,
Simulated = sim_prob_odd
) Quantity Theoretical Simulated
1 P(Y is odd), lambda = 0.8 0.3990517 0.3972