Taller variable aleatoria 2
JuanDev
2025-04-01
Ejercicios
(1). Un sistema de producción tiene fallas según un proceso de Poisson con una tasa de 3 fallas por día. Simular el número de fallas en un semestre (150 días) y calcular la media y desviación estándar.
n <- 150
tasa <- 3
poisson <- rpois(n, tasa)
poisson## [1] 1 3 4 6 2 4 2 1 2 2 7 4 7 1 4 5 4 1 4 1 0 1 5 1 0
## [26] 4 7 3 3 3 1 1 2 3 5 4 6 0 3 4 1 1 3 1 7 6 3 4 3 2
## [51] 3 1 5 4 3 4 4 2 3 1 1 5 5 5 1 0 2 10 4 2 4 3 2 5 2
## [76] 3 2 4 5 4 2 6 3 1 2 3 5 2 2 6 3 3 1 0 1 2 3 3 3 0
## [101] 5 5 4 2 4 6 2 4 1 3 4 3 4 3 0 5 7 3 5 3 5 4 1 2 2
## [126] 4 2 3 0 1 2 2 2 5 2 5 1 2 5 1 2 3 1 6 6 1 6 3 2 4media <- mean(poisson)
desviacion <- sd(poisson)
media## [1] 3.066667desviacion## [1] 1.852503(2). La vida útil (en horas) de un componente electrónico sigue una distribución exponencial con un promedio de 500 horas. Simular 1000 componentes y estimar la probabilidad de que un componente dure más de 700 horas.
n <- 1000
media <- 500
exponencial <- rexp(n, 1/media)
round(exponencial,1)## [1] 690.7 402.5 940.8 427.8 1701.2 82.6 475.2 419.5 83.5 166.6
## [11] 83.4 328.7 289.7 932.7 1514.2 169.5 1180.6 462.8 52.1 617.8
## [21] 213.3 525.9 353.4 440.1 1053.7 479.8 133.0 253.8 72.4 152.2
## [31] 208.4 172.9 322.5 240.0 348.1 253.2 182.4 588.9 8.3 1040.4
## [41] 469.4 102.1 48.5 87.4 247.8 58.4 203.8 235.0 252.0 15.2
## [51] 9.4 535.2 648.6 1042.9 906.6 147.9 869.3 599.4 372.4 443.6
## [61] 107.7 339.5 44.3 24.6 36.2 128.3 57.6 400.4 1424.2 177.2
## [71] 663.7 155.9 537.8 447.6 560.8 437.4 1944.2 708.0 1276.3 141.1
## [81] 1432.7 271.5 905.1 538.1 206.8 221.0 45.6 6.8 351.3 687.1
## [91] 138.6 858.7 623.0 1414.8 235.5 383.4 429.5 1332.4 142.3 367.8
## [101] 743.5 132.8 227.5 413.1 557.3 991.8 962.5 124.6 490.2 1612.5
## [111] 588.5 302.7 1219.2 565.6 387.0 149.5 455.6 377.9 13.8 503.5
## [121] 151.4 371.5 436.9 84.7 57.1 1031.8 125.3 530.9 609.7 1665.3
## [131] 337.0 1528.0 514.2 532.3 22.1 125.3 482.6 114.8 299.8 318.9
## [141] 388.7 42.7 477.4 364.9 1111.1 447.8 902.5 85.9 21.2 381.0
## [151] 751.1 1137.7 801.6 329.9 533.1 187.0 473.0 386.1 210.5 1315.6
## [161] 177.9 642.6 74.0 546.5 276.3 114.9 1171.9 2.2 1069.7 248.9
## [171] 545.2 223.6 1493.2 891.7 315.1 501.1 77.6 295.0 1593.0 468.9
## [181] 524.9 381.2 769.9 696.2 680.0 905.2 205.0 163.7 262.4 204.0
## [191] 28.2 1075.5 621.3 842.3 231.1 57.3 135.3 135.3 638.1 378.0
## [201] 363.0 312.0 467.9 102.8 12.2 104.9 48.2 1246.0 6.6 285.2
## [211] 436.6 336.7 495.5 116.3 691.6 84.6 262.3 809.5 934.4 1033.3
## [221] 318.2 452.4 555.4 267.9 129.7 284.9 180.9 34.5 229.7 316.8
## [231] 78.1 542.8 136.0 163.5 514.9 382.0 1831.8 81.2 1065.8 410.8
## [241] 437.9 925.1 775.6 730.5 874.2 166.1 1959.8 782.5 70.8 63.8
## [251] 514.3 638.2 704.8 57.3 122.5 409.2 1319.6 613.2 17.3 366.8
## [261] 252.6 355.8 530.0 523.4 339.9 151.1 1224.3 88.4 20.9 860.7
## [271] 1555.6 224.3 117.9 440.2 2146.0 178.0 436.7 1206.1 339.7 207.6
## [281] 31.3 175.2 731.4 45.4 655.9 868.4 872.1 217.5 199.9 249.7
## [291] 728.4 430.8 553.4 18.7 549.7 722.9 584.9 643.6 813.5 643.2
## [301] 909.7 182.8 419.4 136.4 34.7 541.2 2249.2 782.1 90.7 337.9
## [311] 835.0 262.9 526.8 1586.5 336.9 76.8 223.1 790.6 737.7 285.3
## [321] 57.8 296.0 852.9 514.5 177.1 332.0 162.8 7.6 556.4 307.0
## [331] 96.3 620.8 2631.6 1277.0 641.9 192.4 149.2 507.2 418.6 1377.3
## [341] 958.7 534.4 2498.1 487.7 38.6 173.0 630.3 70.3 207.6 104.4
## [351] 370.2 823.6 231.1 1188.1 904.8 354.4 107.5 195.5 291.1 32.2
## [361] 2074.5 271.2 222.6 2.2 356.2 68.1 567.9 483.3 245.6 512.2
## [371] 40.5 481.7 509.4 434.7 310.6 473.0 103.6 54.8 107.1 18.2
## [381] 679.4 776.0 465.2 659.8 1074.2 365.5 599.5 1735.8 272.3 20.1
## [391] 774.2 228.9 107.0 768.2 330.0 815.3 185.0 442.0 158.0 30.7
## [401] 2502.6 127.8 2437.4 274.5 580.1 1071.9 396.7 1004.7 484.2 62.2
## [411] 116.9 407.5 233.0 987.6 134.3 52.0 876.6 141.8 464.7 625.1
## [421] 2617.8 825.2 192.4 782.0 177.4 423.2 710.5 430.2 46.6 341.4
## [431] 724.9 690.7 687.3 447.7 232.2 64.8 1662.1 325.7 486.3 67.3
## [441] 841.4 47.6 796.8 146.0 350.6 145.1 56.5 242.2 282.9 913.4
## [451] 138.5 84.6 220.4 921.0 562.8 216.3 1548.1 72.1 818.3 109.3
## [461] 169.3 1552.0 6.7 212.5 18.1 381.8 678.6 591.7 145.7 1371.6
## [471] 298.6 272.0 235.8 2271.2 154.7 252.5 442.7 1221.0 365.2 1082.9
## [481] 1163.7 151.7 264.2 408.1 1214.8 324.0 743.5 427.5 489.7 2613.5
## [491] 2025.1 177.8 204.6 75.8 52.0 198.6 677.7 464.4 989.6 226.7
## [501] 234.5 17.8 1540.5 676.6 841.2 64.8 468.9 866.2 85.0 116.0
## [511] 755.6 199.5 1669.1 49.3 162.5 625.9 4.6 177.7 2168.1 1090.2
## [521] 275.7 498.9 401.0 258.3 630.8 24.6 386.3 110.2 117.5 421.9
## [531] 145.0 213.7 362.7 866.9 229.7 305.8 991.5 651.2 13.0 797.5
## [541] 434.7 222.4 116.0 75.9 388.2 38.3 246.3 5.6 140.5 285.2
## [551] 421.1 367.4 42.3 860.4 695.9 924.1 588.8 73.6 64.8 878.4
## [561] 48.2 448.4 445.3 54.5 102.3 297.5 291.7 189.9 794.9 385.2
## [571] 702.0 284.4 754.5 49.9 96.6 124.0 502.9 92.6 960.4 218.0
## [581] 669.3 45.8 303.8 110.6 408.9 121.2 144.9 276.8 1362.2 1092.8
## [591] 180.6 705.7 554.9 512.3 956.8 1277.6 9.0 125.2 228.0 243.4
## [601] 350.8 158.7 445.9 915.3 231.8 123.8 537.6 714.5 658.3 1579.1
## [611] 392.7 232.4 453.1 764.6 145.1 1245.1 174.0 38.4 26.7 256.0
## [621] 720.7 862.0 233.4 363.8 381.0 1719.9 506.7 86.8 27.8 434.0
## [631] 600.5 730.4 325.2 20.1 680.7 703.8 2210.9 447.0 418.2 607.9
## [641] 436.6 198.0 868.8 566.1 812.0 649.5 186.1 607.5 505.6 519.7
## [651] 114.7 306.5 521.9 894.4 180.5 1124.9 208.9 140.2 755.0 165.5
## [661] 465.3 1194.2 262.3 80.1 927.6 157.1 816.9 672.7 362.7 1831.8
## [671] 291.2 483.3 444.7 414.5 34.8 17.5 1486.4 159.9 156.3 788.4
## [681] 1357.0 9.9 1088.6 717.2 455.2 397.5 407.1 910.6 59.8 971.7
## [691] 408.5 203.6 169.1 1902.3 1466.2 181.0 309.6 121.1 1869.3 273.4
## [701] 217.7 463.8 941.9 107.0 559.1 34.8 1331.1 897.7 628.0 70.1
## [711] 203.1 1433.6 582.6 657.7 23.5 201.3 523.3 24.8 167.9 7.4
## [721] 486.7 496.6 744.3 252.5 798.7 530.2 777.2 445.5 995.2 54.3
## [731] 10.0 339.1 358.8 758.8 310.4 429.6 159.3 59.2 161.0 1235.7
## [741] 1722.3 316.3 133.5 88.6 142.7 327.8 150.6 1544.9 517.0 729.2
## [751] 799.8 834.7 113.4 591.5 341.5 195.9 739.8 33.9 711.2 101.5
## [761] 108.5 49.2 5.0 1975.9 1239.2 583.8 72.9 1346.3 308.3 1457.5
## [771] 1876.3 538.2 136.2 146.8 304.2 98.1 527.8 154.4 639.1 150.6
## [781] 304.5 1478.7 89.9 914.2 468.8 50.9 562.5 148.2 331.6 898.2
## [791] 862.4 17.3 854.3 22.8 177.4 357.6 973.8 415.3 371.1 23.5
## [801] 581.0 2224.5 386.7 1111.3 327.3 191.2 165.9 524.1 414.8 66.6
## [811] 212.6 498.6 281.9 249.5 110.3 104.0 77.1 67.8 123.4 412.2
## [821] 30.7 2013.1 787.2 219.0 440.5 393.7 548.5 345.5 1261.8 72.6
## [831] 92.2 425.2 1210.8 1109.7 302.0 38.3 109.2 604.7 711.1 250.0
## [841] 157.0 482.0 1075.2 1027.7 619.1 1929.8 538.7 92.6 753.7 250.3
## [851] 52.7 577.0 128.5 47.7 1109.7 288.8 290.7 201.0 1235.4 87.0
## [861] 527.1 1650.8 470.8 123.5 430.2 89.1 716.4 922.8 673.3 407.5
## [871] 6.1 269.5 788.6 1042.7 528.8 514.4 263.1 653.9 110.1 41.1
## [881] 323.6 365.2 15.1 22.0 595.1 429.5 1159.7 23.4 549.6 231.8
## [891] 1007.5 88.2 143.6 107.3 30.5 328.2 122.4 220.5 277.7 1209.9
## [901] 659.6 397.1 638.0 206.2 199.0 505.3 660.8 100.7 99.9 826.6
## [911] 95.8 123.2 33.0 358.7 1307.8 113.6 989.7 45.6 1457.4 586.1
## [921] 391.7 303.7 488.9 274.1 454.7 28.0 1285.9 383.1 309.5 188.2
## [931] 35.4 18.8 632.1 720.2 172.8 1942.6 1627.6 1248.8 1688.0 11.0
## [941] 72.0 212.8 335.2 568.4 122.7 251.8 255.8 1498.2 336.2 115.0
## [951] 390.8 365.6 794.3 304.8 937.9 477.6 1220.0 375.8 83.8 101.6
## [961] 595.6 98.8 231.6 68.6 482.6 1222.9 899.0 26.9 2898.1 1017.2
## [971] 1557.4 223.7 225.2 79.5 67.5 502.9 307.8 219.9 144.3 1491.9
## [981] 49.7 1199.8 82.1 1088.8 721.8 609.7 484.4 336.5 812.6 1983.1
## [991] 25.1 891.4 291.2 244.4 532.3 780.0 817.6 224.5 2097.1 713.6prob <- sum(exponencial > 700) / n
prob## [1] 0.251(3). En una línea de ensamblaje, la probabilidad de que un producto sea defectuoso es del 5 %. Simular 100 lotes de 50 productos y calcular el número promedio de productos defectuosos por lote.
n <- 100
lote <- 50
probabilidad <- 0.05
binomial <- rbinom(n, lote, probabilidad)
binomial## [1] 1 2 3 0 3 2 2 1 1 3 1 2 4 4 3 3 3 3 4 4 1 3 5 3 4 5 1 1 2 1 5 2 4 1 3 2 1
## [38] 5 5 4 3 1 2 2 1 2 3 3 2 0 1 3 2 1 5 2 1 2 0 2 0 0 3 2 1 4 4 3 1 1 4 2 0 0
## [75] 4 5 2 5 2 2 3 6 0 1 2 0 2 3 3 3 4 3 1 3 1 4 3 2 3 1(4). La demanda diaria de energía (en MW) sigue una distribución normal con media de 100 MW y desviación estándar de 15 MW. Simular la demanda de un año (365 días) y calcular la probabilidad de que un día supere los 130 MW. y realizar el histograma.
n <- 365
media <- 100
desviacion <- 15
normal <- rnorm(n, media, desviacion)
prob <- sum(normal > 130) / n
prob## [1] 0.02739726hist(normal, probability = TRUE, freq = FALSE, main = "Histograma de demanda diaria de energía", xlab = "Demanda diaria", ylab = "Densidad", xlim=c(0, 200))
curve(dnorm(x, media, desviacion), add = TRUE, col = "red")
(5). Una empresa de manufactura electrónica quiere simular el tiempo de vida (en horas) de un nuevo modelo de capacitor. Basado en datos históricos, se ha determinado que el tiempo de vida sigue una distribución exponencial con parámetro β = 1000 horas, que representa el tiempo medio de vida de los capacitores.
- Simular 1000 tiempos de vida del capacitor aplicando el metodo de la transformada inversa.
- Estimar la media y la varianza de los tiempos generados y compararlas con los valores teóricos.
- Graficar el histograma de los tiempos de vida simulados junto con la densidad teorica de la distribución exponencial.
- Calcular la probabilidad de que un capacitor dure menos de 940 horas usando la simulación.
#a)
n <- 1000
beta <- 1000
exponencial <- rexp(n, 1/beta)
round(exponencial,1)## [1] 1426.3 986.3 36.7 3525.1 1104.3 937.3 1669.8 451.5 860.3 377.7
## [11] 394.2 1354.0 1548.4 552.0 604.6 596.3 1225.8 555.3 1393.4 3043.6
## [21] 712.3 530.7 1155.2 228.3 906.5 377.2 855.9 24.8 243.6 310.2
## [31] 49.0 748.5 572.1 173.4 1689.9 64.2 298.7 1801.2 130.9 443.5
## [41] 836.8 3149.0 192.0 239.3 98.2 15.2 608.6 138.6 833.7 675.5
## [51] 398.3 1999.0 359.4 130.3 304.1 949.9 579.2 2015.4 172.7 229.9
## [61] 1229.4 418.2 1632.9 3618.2 796.0 415.4 604.0 2492.6 915.6 314.7
## [71] 1381.4 992.6 294.9 1100.1 146.5 2155.3 1975.0 2181.8 469.6 1060.0
## [81] 745.6 624.6 45.2 2037.8 507.3 398.7 804.3 333.8 90.5 2057.1
## [91] 1175.0 2378.5 1622.7 1278.8 1312.7 1653.7 2071.5 242.3 1021.0 649.6
## [101] 492.8 2900.4 177.1 1376.6 1247.2 191.4 389.2 40.4 36.3 43.1
## [111] 1704.8 119.0 803.6 296.1 1122.5 848.6 926.0 766.2 22.1 1474.8
## [121] 1326.8 129.8 4459.7 263.2 17.5 154.3 1056.9 62.7 1448.6 48.2
## [131] 186.6 604.3 1640.9 3041.1 2291.1 970.6 124.4 1370.1 69.9 490.2
## [141] 1244.1 2304.0 472.2 942.2 128.0 603.0 1125.4 345.5 2617.5 361.4
## [151] 2851.6 1253.0 1422.4 1383.1 111.5 3258.0 48.1 491.0 1182.2 28.5
## [161] 339.3 2365.7 114.0 1713.9 1104.3 661.6 1471.9 4.2 116.8 903.4
## [171] 812.8 411.1 0.1 2804.9 6264.8 644.9 946.3 2186.4 1090.1 2524.7
## [181] 675.6 559.4 165.5 1713.8 293.5 355.7 881.6 384.1 939.5 2070.7
## [191] 1418.1 351.6 91.2 1135.5 658.3 930.2 2139.5 802.4 102.3 672.8
## [201] 142.5 2509.9 83.2 296.0 33.6 550.2 164.0 815.2 393.2 345.5
## [211] 494.9 1234.6 553.7 240.4 475.0 56.6 546.3 460.0 771.1 2379.3
## [221] 1119.5 1469.3 923.7 1554.7 1444.9 1772.8 391.0 445.5 928.1 2283.4
## [231] 243.3 178.0 614.3 406.8 708.6 329.5 751.2 165.4 1181.8 627.2
## [241] 2070.8 911.9 181.8 2744.3 266.5 468.8 77.3 316.6 530.8 10.8
## [251] 1778.6 112.9 698.6 216.9 3314.5 1934.7 294.8 4293.5 662.0 367.0
## [261] 1654.5 270.3 168.1 1617.3 916.9 1494.8 137.2 1337.5 3563.7 35.7
## [271] 979.9 4610.9 943.3 1180.1 183.1 22.9 185.7 885.7 1362.0 1022.1
## [281] 4158.2 3025.0 1519.6 962.4 466.2 3938.9 1015.3 1696.2 283.4 786.3
## [291] 2103.1 758.4 601.0 266.2 2037.9 1481.3 999.0 994.3 74.3 1687.4
## [301] 409.4 2969.3 328.9 1447.3 446.2 1285.3 418.2 192.2 420.2 67.4
## [311] 1909.6 644.7 1841.3 1098.3 518.0 1262.1 63.2 604.3 94.5 28.9
## [321] 529.5 163.3 650.6 588.7 822.7 204.1 308.4 60.5 166.8 849.0
## [331] 2847.7 764.4 1224.3 1199.0 939.8 1202.5 481.1 438.9 69.7 1201.2
## [341] 1322.3 214.6 134.1 1201.6 2623.4 89.2 4631.6 912.9 1441.5 1204.7
## [351] 1147.9 477.7 117.4 480.1 1494.7 3699.3 343.9 218.0 222.0 1124.6
## [361] 116.4 2572.6 426.2 775.6 244.7 2447.3 84.8 153.1 2557.2 1704.8
## [371] 192.0 409.4 1164.6 911.5 316.2 134.4 1471.9 1917.1 255.9 2548.0
## [381] 15.7 661.1 416.6 3165.9 2539.3 1209.9 604.7 1381.9 496.4 87.7
## [391] 449.4 1042.4 1581.9 313.5 1021.8 785.1 314.7 54.1 1795.9 1562.0
## [401] 822.1 732.7 2005.0 1349.0 1432.3 493.4 427.2 119.5 326.6 1121.3
## [411] 639.5 2252.4 1487.0 1265.9 654.3 52.9 326.2 1343.3 572.8 900.4
## [421] 1002.9 1159.3 33.9 292.8 632.7 229.6 267.8 1103.2 122.5 1594.5
## [431] 32.0 334.2 373.2 1876.4 80.4 835.3 181.1 515.1 201.8 150.3
## [441] 308.5 2770.9 6.3 1006.8 626.7 1968.5 962.0 28.0 179.2 108.0
## [451] 157.0 854.7 2347.2 346.9 174.9 1457.0 960.0 3862.9 1989.7 313.4
## [461] 84.5 2965.0 349.1 252.6 671.3 384.9 725.2 1225.3 211.8 119.4
## [471] 4000.0 1587.8 541.0 766.7 35.1 584.7 846.6 1719.1 1184.3 807.9
## [481] 479.8 488.9 2974.2 105.2 505.4 3724.5 627.4 377.5 587.1 435.5
## [491] 302.8 630.9 419.5 1343.7 8.4 118.4 1109.4 3840.6 2632.0 3649.5
## [501] 86.7 193.5 1009.0 1205.5 489.1 324.9 518.4 475.3 172.4 742.8
## [511] 805.4 1910.5 848.5 1349.4 847.9 92.4 614.2 1344.8 2690.3 726.7
## [521] 2582.8 797.7 1112.4 1237.5 111.3 2569.3 773.6 537.8 603.5 294.9
## [531] 68.3 1040.5 492.6 1405.9 1236.4 1842.4 1587.3 744.2 474.2 816.5
## [541] 67.9 2747.3 269.7 3497.3 752.8 775.7 513.7 427.4 114.9 130.7
## [551] 413.5 892.3 1165.6 61.1 2559.9 2378.7 559.7 315.6 392.7 466.2
## [561] 183.6 186.1 2131.8 716.4 672.4 287.7 43.9 1066.3 979.2 618.0
## [571] 1800.2 155.5 1006.6 133.4 515.5 2538.0 852.3 851.6 2862.8 764.1
## [581] 1832.0 1499.3 54.3 85.0 2666.9 1092.7 1327.6 129.3 1855.1 869.1
## [591] 1249.0 2664.3 33.5 695.5 356.7 1628.0 1855.9 876.1 783.1 1823.2
## [601] 339.3 1511.9 1335.9 269.9 145.2 3505.2 2514.2 1936.3 82.6 143.6
## [611] 1197.6 600.3 57.3 1659.2 592.6 105.1 30.8 133.8 542.4 1492.9
## [621] 1519.9 92.9 93.7 352.2 1479.9 6.4 1048.4 307.8 1567.4 162.2
## [631] 1412.9 41.0 1478.6 563.9 1546.2 426.7 98.8 2135.1 1254.9 612.0
## [641] 83.9 561.0 763.8 20.8 291.0 1147.6 700.0 643.0 39.5 847.4
## [651] 667.8 1376.5 1367.1 1035.5 16.7 2424.4 1372.0 760.9 702.9 1195.5
## [661] 639.4 1072.9 537.9 658.2 393.7 281.6 1404.4 114.8 1098.7 294.0
## [671] 266.8 461.0 329.8 196.1 1780.2 896.1 1280.6 1555.3 265.5 814.9
## [681] 401.8 825.1 870.9 1021.3 428.1 3722.0 3711.4 50.5 1490.4 928.2
## [691] 238.0 421.3 750.5 1477.2 1947.8 436.1 1457.5 380.0 292.3 1611.7
## [701] 762.2 2766.7 1460.4 1404.1 2497.1 446.8 347.3 1290.4 1436.0 407.6
## [711] 249.6 57.6 360.7 35.8 2325.1 459.2 815.8 196.1 416.8 217.2
## [721] 152.6 1365.9 47.6 1214.5 732.9 801.3 446.4 866.8 423.4 168.1
## [731] 2073.1 319.6 372.8 946.8 1490.6 938.9 43.3 1389.6 885.1 2577.1
## [741] 47.5 5023.9 533.8 654.3 858.1 360.7 979.5 610.2 338.0 101.5
## [751] 1498.5 704.4 288.2 233.1 89.5 1.7 210.4 2494.3 459.8 1880.2
## [761] 2074.8 1717.9 2078.3 781.9 1031.8 543.5 1878.8 373.7 3017.5 1167.9
## [771] 344.9 491.0 173.1 947.5 104.4 113.4 34.1 295.6 434.4 411.6
## [781] 337.2 285.2 652.1 1191.0 197.7 344.7 70.0 2333.9 262.3 2632.8
## [791] 594.5 0.7 96.2 314.2 347.7 680.5 808.7 1187.8 688.8 135.6
## [801] 44.5 1303.0 744.2 3750.0 214.2 464.9 4725.6 359.5 372.5 702.3
## [811] 2212.2 225.0 228.4 55.8 1569.5 376.6 668.2 309.8 138.3 926.6
## [821] 1630.7 947.5 28.0 8.7 846.1 1191.7 104.3 866.6 1894.3 1226.9
## [831] 1266.9 10.8 1320.9 2710.6 377.5 2966.4 358.3 180.4 336.4 1060.6
## [841] 407.9 731.4 230.6 836.7 996.7 2299.1 3.5 28.3 141.4 959.7
## [851] 3708.0 1817.4 2066.0 309.7 1380.7 240.2 947.5 568.6 79.0 1331.4
## [861] 922.4 1631.5 2534.3 465.3 223.3 1717.7 446.0 280.0 1929.6 472.8
## [871] 70.0 4305.9 482.7 1424.6 539.1 899.4 2241.7 663.9 433.2 2692.0
## [881] 1327.8 716.2 3428.9 3289.5 974.6 1469.3 260.2 1395.9 149.0 796.0
## [891] 2248.0 1240.3 260.2 703.3 1097.6 1714.4 103.4 99.2 430.5 784.8
## [901] 851.3 1798.2 1813.1 1795.0 114.2 1095.0 239.5 617.5 722.5 116.1
## [911] 3518.2 24.1 797.6 245.1 2879.2 329.1 3167.0 599.2 2505.2 5381.6
## [921] 423.1 1625.4 289.6 274.6 1495.0 2236.6 1075.3 657.4 381.7 605.1
## [931] 454.6 1393.9 90.8 99.0 419.3 580.0 1142.4 544.4 936.0 3287.1
## [941] 207.1 4213.1 2247.8 623.0 1356.4 826.3 347.1 2303.2 2334.5 3977.6
## [951] 838.5 1132.1 600.2 2072.8 407.3 1345.7 325.2 851.8 1314.9 1771.9
## [961] 765.0 132.7 2908.2 833.2 382.7 65.7 1692.1 76.9 815.8 613.2
## [971] 334.5 935.0 1097.5 1514.4 1710.3 1536.9 823.6 683.3 107.9 1122.2
## [981] 913.2 1880.9 139.7 1090.6 1635.9 1657.7 747.6 625.2 2073.2 285.4
## [991] 1779.2 177.8 2106.3 431.8 72.6 1437.0 346.4 3.9 288.9 883.4#b)
media <- mean(exponencial)
varianza <- var(exponencial)
media## [1] 967.6932varianza## [1] 848587#c)
hist(exponencial, breaks = 20, probability = TRUE, freq = FALSE, main = "Histograma de tiempos de vida", xlab = "Tiempo de vida", ylab = "Densidad", xlim=c(0, 8000))
curve(dexp(x, 1/beta), add = TRUE, col = "red")
#d)
prob <- sum(exponencial < 940) / n
prob## [1] 0.616