Taller Generacion VA
Andres F. Montalvo V.
2025-04-02
Simulación de Variables Aleatorias en R
Ejercicio 1: Simulación de fallas en un semestre
Se simula el número de fallas diarias con distribución de Poisson y se calculan la media y desviación estándar.
set.seed(123) # Para reproducibilidad
# Simular el número de fallas diarias con distribución de Poisson
fallas_diarias <- rpois(150, lambda = 3)
# Calcular estadísticos
media_fallas <- mean(fallas_diarias)
desviacion_fallas <- sd(fallas_diarias)
# Mostrar resultados
print("Simulación de fallas diarias:")## [1] "Simulación de fallas diarias:"print(fallas_diarias) # Muestra todos los valores simulados## [1] 2 4 2 5 6 0 3 5 3 3 6 3 4 3 1 5 2 0 2 6 5 4 3 8 4 4 3 3 2 1 6 5 4 4 0 3 4
## [38] 2 2 2 1 2 2 2 1 1 2 3 2 5 0 3 4 1 3 2 1 4 5 2 4 1 2 2 4 3 4 4 4 3 4 3 4 0
## [75] 3 2 2 3 2 1 2 4 2 4 1 3 7 5 5 1 1 4 2 4 2 1 4 1 3 3 3 2 3 6 3 5 5 3 2 1 6
## [112] 2 1 6 4 1 3 6 3 2 4 2 2 2 2 7 1 1 1 4 3 5 4 4 3 4 5 4 7 3 2 2 0 1 5 2 2 1
## [149] 2 4print(paste("Media de fallas diarias:", round(media_fallas, 2)))## [1] "Media de fallas diarias: 3"print(paste("Desviación estándar:", round(desviacion_fallas, 2)))## [1] "Desviación estándar: 1.66"Ejercicio 2: Vida útil de un componente electrónico
Se simula la vida útil de 1000 componentes con distribución exponencial y se estima la probabilidad de que duren más de 700 horas.
# Establecer semilla para reproducibilidad
set.seed(123)
# Parámetros
lambda <- 1/500 # Tasa para distribución exponencial (inversa del promedio)
n <- 1000 # Número de componentes a simular
# Simular la vida útil de 1000 componentes (en horas)
vida_util <- rexp(n, rate = lambda)
# Estimar la probabilidad de que un componente dure más de 700 horas
prob_simulada <- mean(vida_util > 700)
# Mostrar resultados
print("Simulación de la vida útil de los componentes:")## [1] "Simulación de la vida útil de los componentes:"print(vida_util) # Muestra todos los valores simulados## [1] 421.7286305 288.3051354 664.5274339 15.7886796 28.1054880
## [6] 158.2506082 157.1136461 72.6334020 1363.1182322 14.5767235
## [11] 502.4150288 240.1073638 140.5068138 188.5589155 94.1420204
## [16] 424.8930649 781.6017698 239.3802082 295.4674177 2020.5058557
## [21] 421.5748656 482.9356055 742.6378970 674.0222429 584.2644921
## [26] 802.9261715 748.3714344 785.3262734 15.8838720 298.9248456
## [31] 1083.9198727 253.3078643 129.7789087 1298.4460582 614.5128659
## [36] 395.3408794 314.6400389 627.3205015 294.3423211 564.6450169
## [41] 210.1824014 3605.5037880 422.8609826 112.7710033 550.1694088
## [46] 1124.1528462 681.8671496 288.1958340 1362.6379249 656.0815213
## [51] 45.2956751 153.1019250 533.6065348 156.7581280 487.3200753
## [56] 943.9116576 282.2943013 1288.4806645 523.8478740 512.2206709
## [61] 513.9348078 142.3342303 781.5259443 21.0441465 49.3154449
## [66] 49.2846561 140.1925807 147.8934793 486.2148245 462.0136120
## [71] 821.2022634 809.9563838 1268.0727699 760.7748117 190.0071015
## [76] 119.2564834 233.2437118 21.1357258 159.8384497 321.8054601
## [81] 286.2815517 108.0277513 2249.3366989 928.5452766 342.7293189
## [86] 719.7263131 865.5769918 622.3916500 731.6502800 768.6969893
## [91] 2.2995633 554.3827340 149.9851588 596.0015035 557.4643519
## [96] 33.6879455 240.3343604 785.2271695 129.9730535 928.4611437
## [101] 231.6098104 118.0178733 591.0497107 29.8356859 201.6192207
## [106] 471.4699201 208.2903222 376.6092025 94.3431940 438.4269356
## [111] 95.0189103 489.5391031 161.6879136 660.2387768 159.2303242
## [116] 802.5336479 72.8670582 901.5646593 15.0297272 651.7202747
## [121] 99.8961224 875.7281210 881.8341661 421.5217891 174.3763881
## [126] 1648.9123999 200.8530875 550.3508672 664.4615861 320.9513240
## [131] 97.9168577 228.3944283 186.3750820 1731.7974455 637.0138596
## [136] 540.7425753 148.4795804 42.0803672 1476.7004586 984.1261273
## [141] 331.9275628 804.6960719 303.4185420 46.8261566 162.3176420
## [146] 879.9411561 133.0553598 470.3130838 224.5543464 644.4532396
## [151] 89.1445313 785.8630438 31.0703989 285.2916713 865.3904227
## [156] 655.3719523 647.4364831 233.6553545 16.4448943 76.5190213
## [161] 519.2360021 541.2228531 1873.6455691 2.8130456 2.1836853
## [166] 849.9920805 270.3340743 235.1843058 25.7797078 258.5931695
## [171] 741.5715046 639.7427795 713.2340870 1059.1471707 712.0801870
## [176] 442.0571555 1345.4934293 1114.9535486 261.4022301 34.3252824
## [181] 284.5752665 2182.9554679 279.0658828 229.3906519 130.1318528
## [186] 349.4208725 481.5941943 365.7397774 556.1397853 302.8122729
## [191] 335.7088370 815.8294151 50.9630658 203.9920613 1370.1742766
## [196] 1425.9387291 12.0866861 237.7974030 334.0543092 475.1151511
## [201] 568.8875013 41.3825433 821.4538524 79.4502074 739.3079688
## [206] 56.5158695 112.0628352 335.2553200 768.4153551 964.4109681
## [211] 106.7861002 283.9464787 966.6619002 1801.3739315 659.7893229
## [216] 465.3820675 157.7284312 72.3910260 464.1472557 129.1712330
## [221] 269.1939112 37.6771830 64.2188531 1299.4200764 1035.0954970
## [226] 102.6905087 1383.0627398 728.1713857 1381.4611489 741.4170662
## [231] 137.0521309 375.1668631 525.1987506 180.7875512 480.4720864
## [236] 331.5685980 788.8187067 961.2404555 111.5015747 1922.6029448
## [241] 96.2635446 490.4483417 104.9788440 622.9829178 835.0475505
## [246] 195.3443616 505.6684171 37.4918213 1335.2873576 837.8102313
## [251] 412.5593318 83.8723360 231.7076589 855.2308250 245.5730827
## [256] 781.4836148 562.6875171 173.3324814 23.8226017 546.1771758
## [261] 713.3149203 259.0694156 812.7940837 1097.0087203 84.9365573
## [266] 388.1296292 791.1763522 310.3980662 1291.0536276 322.0300712
## [271] 576.1389134 346.7348680 767.7182029 313.9337213 462.1013389
## [276] 187.7426857 40.1261741 178.2238574 635.7549329 1103.6325925
## [281] 376.7047564 17.1687135 286.9273527 553.7857422 579.4564802
## [286] 420.7738517 1179.5040694 577.4821294 905.2024390 36.0537206
## [291] 3.9487120 118.2929428 1199.9702239 137.1255285 880.1208045
## [296] 368.2864251 315.0814951 448.8586392 575.9156463 470.7991741
## [301] 1484.2137992 18.8049234 179.0134157 8.8468795 452.3488395
## [306] 154.9312163 316.4781388 1518.2815268 239.0316855 544.0125777
## [311] 329.2508235 35.5413917 395.6643175 300.9482119 1272.8783292
## [316] 332.1077742 400.2837352 253.1100996 28.2341582 302.2382171
## [321] 616.9207995 501.7683883 1012.9019925 69.3826627 183.5849145
## [326] 165.7351425 29.8924586 9.8428994 1750.0033405 1649.6541201
## [331] 69.6892311 150.2615004 153.7666824 637.0811132 312.3048285
## [336] 47.0234177 191.7640152 87.4613670 592.3074021 673.1844065
## [341] 1820.5186305 66.7340828 628.2868647 582.3654858 52.4498134
## [346] 166.7051578 21.0655139 30.6243865 8.3706297 521.5635849
## [351] 11.0805219 186.4903511 753.4453766 301.4295837 778.2754125
## [356] 322.7173917 508.5692475 594.9123660 129.7454238 1312.7907151
## [361] 1936.6668415 202.3777822 254.8654536 15.3002078 275.4075914
## [366] 600.2064240 1560.0231401 575.3957536 394.0761299 105.5239610
## [371] 259.1353394 344.8346243 382.6444968 953.7835313 318.9553833
## [376] 682.1277938 93.8384931 298.8235578 31.3032490 125.7436371
## [381] 245.6362173 1222.7484295 447.6088127 114.5621573 252.9320579
## [386] 164.8825608 236.6203461 19.5405903 2.9083041 547.6631364
## [391] 345.5561229 306.4351638 1121.2587436 1139.3747804 54.4702174
## [396] 887.2181652 1875.2362457 21.3138463 1229.9439171 412.5782824
## [401] 687.4433923 87.2781242 306.6944296 1001.1280160 501.8881582
## [406] 214.7548106 331.2219789 190.8292142 22.3357661 875.9402018
## [411] 360.3605085 134.8005098 39.5609140 753.5613803 413.9971440
## [416] 83.0305952 853.2507494 1310.1296564 469.8711534 366.8385376
## [421] 1973.4917012 115.9593510 46.4262587 599.4625767 936.6392409
## [426] 527.0837939 159.6213372 229.3609313 347.8504463 37.3907434
## [431] 210.6709817 212.3732430 1964.2178220 680.4026896 224.3533793
## [436] 882.0475647 478.1991686 304.2562793 0.4129869 786.5567477
## [441] 1676.1231161 97.3534826 489.2304772 27.9290003 295.4220204
## [446] 1091.1815455 195.0206973 86.4377357 830.8891011 1112.7612190
## [451] 57.4375831 359.2943520 1008.1224348 13.7811392 860.2850364
## [456] 69.3526887 769.7564410 775.9822309 671.1398163 183.0102825
## [461] 153.4278204 234.2456244 307.4991093 705.4048590 348.1306582
## [466] 509.6675735 661.1121702 135.3675770 308.6120449 364.1759930
## [471] 319.4671399 2239.3398271 1006.8155871 1833.4509012 412.8389847
## [476] 188.0271292 862.7699318 661.8349058 1369.4133059 407.7039398
## [481] 569.5060314 365.0632724 388.6032815 1638.1932496 372.1661987
## [486] 165.6004964 167.6402313 1676.9439093 195.1052444 573.0967237
## [491] 48.2443058 436.5921328 697.4783223 89.9016238 61.6756089
## [496] 188.7211201 469.1152083 105.5868415 26.2900780 1503.9753347
## [501] 2451.7035120 271.9094823 577.5668696 72.0737206 203.8129501
## [506] 157.2210605 425.2778804 1317.6364162 212.3537724 1130.7851574
## [511] 3.1815268 713.3255619 499.0398837 226.3988883 151.1226072
## [516] 26.0433337 14.6810925 147.4421436 440.4310670 822.3283272
## [521] 1215.6702434 755.7319384 872.2233809 261.9853232 27.3949406
## [526] 4.5196765 193.1989014 37.1854938 51.4986565 245.3418423
## [531] 103.1829561 365.4269306 889.1880372 169.6035459 46.5227943
## [536] 311.4636578 259.1668020 1875.0588697 608.3809905 1700.3761790
## [541] 297.9029373 188.0502653 83.5628633 168.3236435 11.3145965
## [546] 262.7505893 24.7563926 2790.6793839 184.1724414 614.4469334
## [551] 485.6800493 308.3862553 1557.0063367 574.0589797 237.2249344
## [556] 542.6036957 54.6818294 742.1216508 284.9315563 70.7342430
## [561] 96.3629608 54.9972077 8.2098581 134.8761561 1283.1273348
## [566] 840.3840214 657.4065806 530.2024786 677.0884967 454.6785285
## [571] 60.2805375 816.6437828 15.2376712 21.2320042 666.4654473
## [576] 502.3930455 123.2613835 753.0589047 190.0195670 1205.5109875
## [581] 281.9689147 1622.7191388 319.8446678 385.3904852 412.2744193
## [586] 143.2215595 2.4254795 684.6650401 593.2274427 127.1107006
## [591] 47.7780687 806.1666926 958.3959281 376.8014969 72.1486795
## [596] 646.9119470 65.4653807 329.6238787 142.1138195 629.5710937
## [601] 209.5798547 1134.5511842 833.8864343 165.6229484 273.6921224
## [606] 437.3737513 1064.7456655 464.7324390 933.7084554 6.9977269
## [611] 1846.9809321 273.6860395 59.6650792 141.4626392 443.3451888
## [616] 292.7383417 85.5655763 636.0915620 311.2373496 483.6997781
## [621] 81.4473382 439.7337670 848.2631713 714.2997281 121.7259828
## [626] 47.9942833 790.1240354 59.5458692 501.7450180 219.5872827
## [631] 430.6028102 1146.6074483 629.1637728 2418.3673652 245.6705569
## [636] 326.7154903 186.9455143 399.4533578 159.1979258 793.0526341
## [641] 885.3193353 459.1961079 586.3881437 1161.4932054 213.1501888
## [646] 50.9227291 736.6087660 194.7615896 221.8585593 128.9277608
## [651] 389.3915997 1856.0522215 631.2360982 880.8945100 485.8578290
## [656] 673.6837188 259.3356967 390.3540005 1049.8880668 373.9548730
## [661] 1084.5730389 257.0985334 69.2841414 300.9178487 227.7627103
## [666] 951.0805914 29.4057564 98.6385469 228.9230512 1118.0134182
## [671] 326.3315787 450.2416446 784.8107370 68.5687540 1001.8854513
## [676] 964.3696881 218.6117452 473.6093813 746.7076899 1583.2653065
## [681] 1226.9592958 319.6825185 202.9795039 67.7483736 221.3092663
## [686] 252.4442135 609.4187838 422.5941528 31.6833272 365.8657330
## [691] 331.7903178 657.3013598 1120.7761755 75.2701634 125.6683154
## [696] 128.4048038 503.0509187 748.7851483 207.6377718 128.9180095
## [701] 1066.1873398 72.7797811 598.2604637 1022.6091798 387.7085214
## [706] 1119.4739686 190.9898499 420.4888288 790.7971628 139.2580701
## [711] 75.0893754 220.0504579 641.0656008 1291.7319116 134.8964050
## [716] 2907.1641488 1035.2401398 179.0228095 46.7861865 621.5701056
## [721] 288.4719290 192.9136666 94.2729714 1195.4748890 2067.9950443
## [726] 973.8329080 38.0543325 616.9707761 169.5061966 218.0918090
## [731] 369.0146217 285.3486184 42.1882898 679.6682807 27.3693245
## [736] 610.9319106 302.1827079 984.8417276 119.8009505 1346.7762559
## [741] 1532.3865711 424.9213001 2519.6984344 401.6937506 496.9798764
## [746] 88.7062766 708.0904914 468.9116264 1167.6642121 490.0617730
## [751] 124.9055369 443.3659813 70.7131934 1560.3425539 956.0170024
## [756] 227.0864707 326.6900503 10.7210753 67.7261658 3210.9420214
## [761] 768.2595932 28.6134832 86.2019891 1394.4114930 778.8413576
## [766] 203.0729740 1064.2064390 121.8070623 30.4619522 2065.2106878
## [771] 225.2279520 542.7974591 54.5631796 237.6522073 123.1291620
## [776] 468.6304019 630.9665595 1001.4970023 210.3113041 62.5168087
## [781] 398.3716159 235.5584037 49.2797939 538.8276782 14.9656348
## [786] 315.7679476 26.2725693 1005.3073801 105.1244935 270.5970469
## [791] 233.4485550 338.9059983 69.0488424 2073.8547769 534.6525042
## [796] 55.1138069 1127.0359502 739.1563775 184.6086963 1336.6962605
## [801] 1008.2908012 578.5338669 346.1957576 730.4415594 279.0688686
## [806] 356.7849570 48.0433260 1428.7186935 306.1094761 522.0792047
## [811] 123.7636534 615.3306355 350.8207194 12.5749717 487.2778267
## [816] 81.4331577 117.3444083 405.6189796 247.7865487 343.9147081
## [821] 34.7590470 451.0441134 432.8866529 154.6267448 100.8816656
## [826] 36.3599309 97.4518666 2029.6125737 2545.7577937 718.6601981
## [831] 2027.0152715 1276.7563862 414.7296301 748.1541174 336.9779109
## [836] 427.4969727 830.8325279 85.5671042 788.2590890 909.3854194
## [841] 525.0166002 928.7549359 657.6566347 113.5596184 185.6713344
## [846] 323.5256001 594.5378179 6.5267290 469.5135084 1146.1436385
## [851] 65.2327174 21.0848636 130.7656612 576.3404351 365.0319044
## [856] 714.5398769 431.1808987 29.8650061 222.3988681 55.7867383
## [861] 924.9099493 230.1835620 89.5256505 471.5383155 272.7943989
## [866] 519.1699946 144.0784919 34.4308142 667.2487294 450.6684139
## [871] 297.9726312 300.5107120 620.4249826 609.7529805 145.5156142
## [876] 178.9449811 788.2735142 112.7659029 1557.7634647 368.4402147
## [881] 0.6716992 387.0597910 98.8021491 235.8376263 213.5778118
## [886] 1239.0423884 944.3630665 1298.8762275 310.8894788 952.8180742
## [891] 2063.8688308 47.6982259 507.0238196 1064.3199803 233.0399933
## [896] 638.4367710 509.4640951 38.8531494 313.8505241 16.7445383
## [901] 82.1438972 330.7340622 2083.4346805 265.6896671 475.8988116
## [906] 312.0117444 69.5779729 158.1483086 886.0612507 84.7100895
## [911] 494.2746084 639.2308484 838.7021744 1898.1751156 607.4695294
## [916] 691.2704455 958.8514342 205.3292817 2229.4122859 231.2400930
## [921] 2095.1459377 143.8400021 933.9351828 142.4433756 346.6035691
## [926] 594.1076684 858.2356926 1648.9344089 273.5310560 508.8082491
## [931] 52.8764706 176.3305289 401.2423320 1731.9852150 558.0245431
## [936] 30.6664107 627.2374484 483.5725720 182.5750542 415.8034054
## [941] 626.7630188 108.2713750 751.0153688 1072.1998728 9.4558073
## [946] 287.3849634 563.8941899 2036.1628559 246.0935980 1821.8080343
## [951] 375.5668575 312.3929838 127.5024416 130.5724860 628.3532907
## [956] 467.4009281 205.4707500 502.2177780 1145.2357144 91.3872421
## [961] 906.4942346 241.3501241 434.3260065 139.1858107 1055.6058434
## [966] 44.3645699 539.7159626 687.8336475 633.1429523 108.8471375
## [971] 537.5410504 348.6780711 1996.9283742 1548.8526261 64.7705361
## [976] 109.0609785 174.7052633 692.6301378 154.3812877 61.8254492
## [981] 361.5784398 1077.6839182 329.0716948 271.0462969 161.8351697
## [986] 285.1829424 34.5530961 400.4964311 222.2220511 559.1839491
## [991] 611.9973571 1397.7927751 21.4452869 1065.5912067 12.8849721
## [996] 142.0699491 285.0783595 646.6990141 135.3428686 419.4169924print(paste("Probabilidad estimada (simulación):", round(prob_simulada, 4)))## [1] "Probabilidad estimada (simulación): 0.255"# Valor teórico para comparar
prob_teorica <- exp(-lambda * 700)
print(paste("Probabilidad teórica:", round(prob_teorica, 4)))## [1] "Probabilidad teórica: 0.2466"Ejercicio 3: Simulación de productos defectuosos
Se simula el número de productos defectuosos en lotes de 50 unidades y se calcula el promedio.
set.seed(123)
# Simular el número de productos defectuosos por lote
defectuosos_por_lote <- rbinom(100, size = 50, prob = 0.05)
# Calcular el promedio de productos defectuosos por lote
promedio_defectuosos <- mean(defectuosos_por_lote)
# Mostrar resultados
print("Simulación de productos defectuosos por lote:")## [1] "Simulación de productos defectuosos por lote:"print(defectuosos_por_lote) # Muestra todos los valores simulados## [1] 2 4 2 4 5 0 2 4 3 2 5 2 3 3 1 5 1 0 2 5 4 3 3 7 3 3 3 3 2 1 6 5 3 4 0 2 3
## [38] 1 2 1 1 2 2 2 1 1 1 2 1 4 0 2 4 1 3 1 1 3 4 2 3 1 2 1 4 2 4 4 4 2 3 3 3 0
## [75] 2 1 2 3 2 1 1 3 2 4 1 2 6 4 4 1 1 3 2 3 2 1 4 1 2 2print(paste("Promedio de productos defectuosos por lote:", round(promedio_defectuosos, 2)))## [1] "Promedio de productos defectuosos por lote: 2.48"Ejercicio 4: Demanda diaria de energía
Se simula la demanda diaria de energía durante un año con una distribución normal y se estima la probabilidad de que supere los 130 MW. También se muestra un histograma de la distribución.
set.seed(123)
# Simular la demanda diaria de energía (en MW) durante un año
demanda_diaria <- rnorm(365, mean = 100, sd = 15)
# Estimar la probabilidad de que la demanda supere los 130 MW
prob_superar_130 <- mean(demanda_diaria > 130)
# Mostrar la simulación completa
print("Simulación de demanda diaria de energía (MW):")## [1] "Simulación de demanda diaria de energía (MW):"print(demanda_diaria) # Muestra todos los valores simulados## [1] 91.59287 96.54734 123.38062 101.05763 101.93932 125.72597 106.91374
## [8] 81.02408 89.69721 93.31507 118.36123 105.39721 106.01157 101.66024
## [15] 91.66238 126.80370 107.46776 70.50074 110.52034 92.90813 83.98264
## [22] 96.73038 84.60993 89.06663 90.62441 74.69960 112.56681 102.30060
## [29] 82.92795 118.80722 106.39696 95.57393 113.42688 113.17200 112.32372
## [36] 110.32960 108.30876 99.07132 95.41056 94.29293 89.57940 96.88124
## [43] 81.01905 132.53434 118.11943 83.15337 93.95673 93.00017 111.69948
## [50] 98.74946 103.79978 99.57180 99.35694 120.52903 96.61344 122.74706
## [57] 76.76871 108.76921 101.85781 103.23912 105.69459 92.46515 95.00189
## [64] 84.72137 83.92313 104.55293 106.72315 100.79506 113.83401 130.75127
## [71] 92.63453 65.36247 115.08608 89.36199 89.67987 115.38357 95.72840
## [78] 81.68923 102.71955 97.91663 100.08646 105.77921 94.44010 109.66565
## [85] 96.69270 104.97673 116.45259 106.52772 95.11103 117.23211 114.90256
## [92] 108.22595 103.58098 90.58141 120.40979 90.99611 132.80999 122.98916
## [99] 96.46449 84.60369 89.34390 103.85326 96.29962 94.78686 85.72572
## [106] 99.32458 88.22643 74.98087 94.29660 113.78495 91.36980 109.11946
## [113] 75.73176 99.16657 107.79111 104.51730 101.58514 90.38941 87.25443
## [120] 84.63807 101.76470 85.78788 92.64164 96.15862 127.65793 90.22075
## [127] 103.53080 101.16941 85.57215 98.93038 121.66826 106.77256 100.61849
## [134] 93.66255 69.20129 116.97006 78.09040 111.09921 128.63655 78.34160
## [141] 110.52677 96.06704 76.41784 77.27999 75.97696 92.03640 78.07367
## [148] 110.31875 131.50163 80.69454 111.81608 111.53563 104.98304 84.87435
## [155] 98.20821 95.79407 108.44484 94.41342 114.65460 94.38129 115.79067
## [162] 84.26234 81.09767 148.61560 93.74714 104.47341 109.54855 92.74329
## [169] 107.75293 105.53447 96.76929 100.97940 99.48899 131.92678 88.87996
## [176] 83.56006 100.56683 104.65721 106.54785 93.12452 84.05011 118.94778
## [183] 94.75524 87.01731 96.45581 97.04236 116.64880 101.27106 111.31081
## [190] 92.51062 103.21668 95.12971 101.41875 86.56955 80.33798 129.95820
## [197] 109.01063 81.23093 90.83251 82.21780 132.98216 119.68619 96.02282
## [204] 108.14791 93.78490 92.85630 88.17096 91.08074 124.76361 99.18958
## [211] 101.78868 103.65531 118.48714 92.25904 85.11239 125.13545 93.38255
## [218] 89.15401 81.45590 80.72926 91.39040 109.26979 116.64772 110.61383
## [225] 94.54514 100.89625 89.43105 89.24173 113.26976 84.76611 129.32941
## [232] 98.64521 103.21808 88.92208 91.38417 80.24476 97.25612 106.28474
## [239] 104.86457 88.27695 88.17067 92.46702 122.44091 82.94045 97.31423
## [246] 128.53543 98.48538 79.60239 90.02846 107.28190 94.36596 91.57185
## [253] 94.84124 101.35745 123.97763 98.67152 116.21199 109.46131 98.29540
## [260] 77.00647 92.18324 92.65194 100.70732 119.50298 134.39618 123.21372
## [267] 98.00274 73.65209 94.16830 101.33811 112.67520 114.43792 110.26464
## [274] 79.07088 112.74465 93.30164 102.62204 101.11827 106.42250 100.37012
## [281] 74.98787 111.04744 105.79040 96.01523 101.77217 102.01058 103.31529
## [288] 124.61269 96.71424 102.52098 117.52576 115.81272 117.17895 91.33798
## [295] 130.03724 101.00051 128.00278 79.73646 100.31475 118.74872 89.27137
## [302] 88.70967 85.92192 84.21230 93.44261 104.96769 69.78684 103.17971
## [309] 118.55013 130.56361 119.51764 111.35162 74.09904 90.97740 94.71930
## [316] 110.55286 98.41493 81.12027 125.26654 113.67087 103.56145 118.27163
## [323] 79.91839 109.91230 92.15631 110.25618 99.08767 109.49441 120.03276
## [330] 100.10935 115.26338 82.17349 89.17593 122.78827 105.66082 69.21666
## [337] 79.53944 96.98828 112.98669 98.47175 109.36281 114.38508 125.06582
## [344] 100.84025 99.22027 73.70144 101.48991 91.42225 85.38986 97.30141
## [351] 115.22415 70.10877 93.59081 101.74956 86.60189 105.00854 106.17145
## [358] 99.50446 63.01153 138.57187 96.92051 109.76790 104.10650 115.37010
## [365] 112.26489# Mostrar resultado de la probabilidad estimada
print(paste("Probabilidad de superar 130 MW:", round(prob_superar_130, 4)))## [1] "Probabilidad de superar 130 MW: 0.0301"# Histograma de la demanda diaria
hist(demanda_diaria, breaks = 30, main = "Histograma de demanda diaria de energía",
xlab = "Demanda (MW)", col = "lightblue", probability = TRUE)
# Agregar línea vertical en 130 MW
abline(v = 130, col = "red", lwd = 2, lty = 2)
legend("topright", legend = c("Umbral 130 MW"), col = "red", lwd = 2, lty = 2)
Ejercicio 5: Tiempo de vida de un capacitor
Se simula el tiempo de vida de capacitores aplicando la transformada inversa, se calculan estadísticas y se grafica la densidad teórica.
# a) Método de transformada inversa
set.seed(123)
u <- runif(1000)
tiempos_vida <- -1000 * log(1 - u) # Transformada inversa de exponencial
# b) Estimación de media y varianza
media_simulada <- mean(tiempos_vida)
varianza_simulada <- var(tiempos_vida)
# Valores teóricos
media_teorica <- 1000
varianza_teorica <- 1000^2
# c) Probabilidad de durar menos de 940 horas
prob_menor_940 <- mean(tiempos_vida < 940)
prob_teorica <- 1 - exp(-940/1000)
# Mostrar resultados
cat("\nProblema 5 - Tiempo de vida de capacitores (Exponencial):\n")##
## Problema 5 - Tiempo de vida de capacitores (Exponencial):cat("a) Se generaron 1000 tiempos de vida usando la transformada inversa\n")## a) Se generaron 1000 tiempos de vida usando la transformada inversacat("b) Comparación de estadísticas:\n")## b) Comparación de estadísticas:cat(" Media simulada:", media_simulada, "vs. Media teórica:", media_teorica, "\n")## Media simulada: 986.1544 vs. Media teórica: 1000cat(" Varianza simulada:", varianza_simulada, "vs. Varianza teórica:", varianza_teorica, "\n")## Varianza simulada: 954966.2 vs. Varianza teórica: 1e+06cat("d) Probabilidad estimada de durar menos de 940 horas:", prob_menor_940, "\n")## d) Probabilidad estimada de durar menos de 940 horas: 0.611cat(" Valor teórico (1 - e^(-940/1000)):", prob_teorica, "\n")## Valor teórico (1 - e^(-940/1000)): 0.6093722# Gráfica: Histograma con densidad teórica
hist(tiempos_vida, breaks = 30, main = "Histograma de tiempo de vida",
xlab = "Tiempo (horas)", col = "lightgreen", probability = TRUE)
curve(dexp(x, rate = 1/1000), add = TRUE, col = "red", lwd = 2)
legend("topright", legend = c("Densidad teórica"), col = c("red"), lwd = 2)