Simulacion de variables 2
Luis Tapia
2025-09-24
- 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.
¨A) Simulación
set.seed(0508) # Semilla para reproducibilidad
fallas <- rpois(150, 3) # 150 días, lambda = 3 fallas por día
fallas## [1] 2 6 1 0 5 4 5 5 1 2 2 6 1 1 3 3 4 2 0 2 2 2 0 4 2 0 1 4 6 1 5 6 4 1 3 4 3
## [38] 1 4 5 4 2 3 3 3 3 3 1 4 3 4 4 2 3 1 3 2 3 3 6 5 2 5 5 2 3 5 4 1 4 1 2 4 4
## [75] 1 6 2 1 2 1 4 0 5 0 3 2 4 3 3 4 4 2 3 4 1 6 5 5 6 3 4 1 2 5 3 3 1 1 1 3 1
## [112] 4 2 3 4 4 2 4 2 5 2 4 5 5 3 2 6 2 3 6 3 3 3 5 8 3 3 3 4 2 3 4 2 6 0 2 6 1
## [149] 3 4## B) Media y desviación estándar
mean(fallas)## [1] 3.073333sd(fallas)## [1] 1.655159## C) Gráfico de barras
barplot(table(fallas),
col = "lightblue",
main = "Distribución de Fallas por Día (150 días)",
xlab = "Número de fallas",
ylab = "Frecuencia")
## D) Total de fallas en el semestre
sum(fallas)## [1] 461- 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.
A) Simulación
vidas <- rexp(1000, rate = 1/500) # 1000 componentes, media = 500
vidas## [1] 64.0543150 858.9153206 313.3451508 953.6276236 230.9221521
## [6] 565.2377347 324.0666434 99.9956023 811.7140744 539.2717847
## [11] 220.1233911 1331.6133851 616.0469102 31.0975129 1316.2530837
## [16] 283.1327560 1563.6362619 689.6081036 69.9405160 542.0515951
## [21] 80.3416504 547.6606819 202.8006238 401.9568320 229.5897265
## [26] 427.8185448 771.1238069 936.5548193 2662.4765627 535.5606191
## [31] 139.1290110 352.0780536 233.5978979 61.0499277 552.8938900
## [36] 838.8377547 1373.5849400 274.7380759 308.7321834 159.5854668
## [41] 804.1340131 378.8140272 613.5968630 395.6994230 67.5038973
## [46] 1752.7972646 18.1102846 127.4639827 286.1042386 34.5636001
## [51] 892.8642729 335.0729987 351.7020754 47.2921967 246.6465393
## [56] 22.9565990 43.5116959 1022.9294812 1055.4856152 119.3582597
## [61] 584.3946100 1425.9010614 227.9670292 78.9432088 66.4146254
## [66] 1584.3909829 796.8111438 370.0295570 378.0125258 253.6843044
## [71] 93.2188944 562.4817847 74.2922744 78.2587714 326.9985386
## [76] 551.1587467 158.7945761 187.1528716 654.2059467 931.4381359
## [81] 86.4339835 608.7625040 329.3548783 34.4265370 2553.9249115
## [86] 327.5771420 45.2367184 700.5638191 74.3854630 624.2898639
## [91] 651.1957650 1599.4206405 105.5010837 344.8775350 93.5024780
## [96] 532.9515137 34.1708142 658.6376796 106.7932329 1152.0314803
## [101] 125.7756038 1474.1069769 136.9822822 151.7615959 451.6279610
## [106] 333.5430608 312.5193152 457.6795925 136.1703835 59.3033545
## [111] 415.1294511 8.4067201 944.6103312 53.7742008 145.7863988
## [116] 13.9481832 204.3725403 478.7957291 816.9390961 416.8947497
## [121] 300.6704368 587.8875959 280.7032906 1817.4141717 956.1150157
## [126] 513.6421313 1636.4256180 1042.1124443 0.0208565 901.0556358
## [131] 329.5679744 288.2095617 386.2246114 117.9791549 689.3601273
## [136] 185.6709508 167.4299099 727.9572108 512.7216079 449.7134527
## [141] 148.4267373 894.7267243 49.5234458 35.2361534 2195.4549792
## [146] 178.3952139 641.4265372 457.1945062 439.8430311 1423.6443308
## [151] 59.8736042 124.1834033 279.4513274 1001.3668388 635.9638651
## [156] 435.5205665 311.3563780 4.6300148 64.7199965 1478.4826816
## [161] 167.4723526 119.0848351 209.4570179 288.5260913 502.2928461
## [166] 1112.7397073 647.2456869 505.5817170 100.0470886 1210.4406123
## [171] 328.0923858 1094.1341286 380.0198450 342.3372416 768.9293921
## [176] 120.5594924 1515.5156724 876.9783005 2224.9604656 14.2632627
## [181] 77.5762396 117.4727446 648.1497488 910.0993434 163.9061692
## [186] 437.5477287 355.3689178 782.0731820 152.2588127 164.3247483
## [191] 1033.1207169 955.0507823 45.9532333 93.8767696 145.1059793
## [196] 238.6223664 2.5451649 20.2622923 14.8156209 536.5098161
## [201] 166.1451568 310.4110395 663.6028983 1246.0594707 351.2494233
## [206] 970.1513536 625.0200034 112.4667964 277.3505170 327.6863343
## [211] 441.0876492 406.8882443 934.6538684 1843.3128026 451.4336997
## [216] 75.6413769 21.4692639 902.9266964 265.1928219 655.6988968
## [221] 144.1187935 44.4102162 520.4787473 177.4290250 680.3318276
## [226] 549.4502662 1708.1534377 306.5234986 440.8632261 282.4107027
## [231] 1172.8264288 340.6078543 172.7117235 58.6824995 262.7070060
## [236] 279.4839158 900.8955662 100.4824636 156.1141353 49.9220510
## [241] 381.0243304 149.4790916 596.0227977 493.1777580 1311.8979604
## [246] 135.3067955 57.5652192 371.2314954 665.5448633 190.3546429
## [251] 424.3049253 136.0344741 118.4195025 44.6907630 1074.5732476
## [256] 183.9451073 329.4802492 156.8779617 237.5316896 1089.4519877
## [261] 158.5682461 194.3558522 331.4539460 23.4488912 619.0245873
## [266] 886.9598731 1268.8708910 435.0570560 475.6159568 178.3388649
## [271] 32.6511734 644.6996596 300.6954091 711.6892365 29.5993134
## [276] 771.3046611 536.1505003 1497.9727056 279.7850955 535.0460713
## [281] 357.0442104 172.0530225 221.9181762 5.5608046 548.4595019
## [286] 225.7226841 213.5455187 508.1869653 225.6116213 99.6921763
## [291] 671.7207674 221.2296049 336.0113797 434.2064424 296.2067944
## [296] 321.9668260 2022.4569392 1030.4918969 247.7207445 132.7382757
## [301] 595.9094623 1294.9958413 526.6388007 219.1619251 165.2817130
## [306] 1103.5651033 42.4555752 453.4144459 527.1062096 421.0118009
## [311] 281.6746421 128.9391872 802.1532353 412.0190429 76.6213734
## [316] 541.4376147 286.6331965 293.0191814 200.4141670 410.0423655
## [321] 1954.2287019 795.7955058 767.8470527 504.6992477 545.9570889
## [326] 26.0691813 1.8348266 201.2283939 50.4287950 450.4439029
## [331] 566.5339795 135.9165560 251.9598396 228.9208223 74.0260235
## [336] 1124.4867043 71.5220036 169.9951212 160.6198107 107.9964135
## [341] 173.4959558 314.2503053 76.4050169 93.5000503 311.7651693
## [346] 743.7618887 1161.0703309 283.2623713 349.6922049 616.9020845
## [351] 317.0717706 1152.1007082 368.4900077 783.7535410 269.6615884
## [356] 181.8646283 1055.7980922 231.0606646 12.0437322 852.3736046
## [361] 612.9413228 467.8486577 6.9100636 292.4888241 684.4498133
## [366] 220.1305639 870.2543499 111.9795877 145.3091001 587.6229731
## [371] 32.3353077 177.2057146 957.8193221 787.0042361 772.1371753
## [376] 204.0115071 207.0616640 168.6282000 279.8463868 38.1953274
## [381] 472.1638390 103.4890278 34.0671373 2374.7610405 696.8282776
## [386] 191.3260634 335.5984872 1757.5924182 162.4534989 255.0280967
## [391] 633.6454339 1016.7376608 5.5288074 118.6340984 253.0115393
## [396] 17.8521036 103.5682911 1040.8692636 214.3586522 340.1217449
## [401] 71.5604874 966.0537345 110.3829068 513.2512725 85.6521199
## [406] 1099.8206888 43.0471765 2106.0574147 24.9129057 502.8637906
## [411] 71.8202288 318.1934985 341.1686586 27.4050201 969.6765286
## [416] 26.3177041 183.5323698 13.6611008 2251.1766198 5.0345368
## [421] 1717.0618176 506.5933233 35.9258332 400.1824148 395.4261201
## [426] 21.5126600 246.6237030 450.7952914 233.4180634 58.2743279
## [431] 8.4897741 435.8254666 55.1097140 130.7642125 2087.7468678
## [436] 638.1928082 23.8272459 79.0985052 388.7610901 216.3486122
## [441] 692.4624857 667.8835936 682.8302345 1524.4416743 1178.0066257
## [446] 691.9812429 375.7296139 450.3214666 102.4461123 836.3388814
## [451] 145.1248650 171.4960386 2904.8052950 291.1215920 1214.6260021
## [456] 1265.9023841 691.4329179 532.2229848 97.8416470 94.0527482
## [461] 79.7773978 1517.3167921 587.6023732 57.3590186 715.7943690
## [466] 457.1306421 49.6285993 22.4010914 206.0213730 1304.0418876
## [471] 918.5347010 82.8519398 311.4077430 621.3271688 67.4407245
## [476] 1612.7038783 235.2924584 1063.2387036 408.5650812 3.7403748
## [481] 296.2637318 197.1000088 1005.9282202 297.1466866 1361.0326601
## [486] 2842.7793903 288.2946189 131.6436410 672.8271842 24.7000712
## [491] 718.9168427 561.7425130 109.0360139 303.6562977 1143.3794004
## [496] 817.0171678 456.6791078 1513.1643684 1158.6163190 434.0329007
## [501] 396.1345210 652.1334280 324.3924084 478.1898949 119.3778845
## [506] 139.5064490 110.6520079 344.8111089 296.2669174 661.9731164
## [511] 1156.0231475 553.8365067 733.3549670 971.9279955 189.0235136
## [516] 86.4287803 67.9464552 666.4775610 41.6245647 346.6642820
## [521] 128.0271111 658.5308187 558.5437584 3176.8750628 905.1630655
## [526] 245.2787554 1683.8224827 1410.1338013 120.9942901 1040.0828753
## [531] 147.1202977 1149.7617781 1566.8200365 41.4093232 124.2937612
## [536] 966.4618885 105.4984599 207.3761132 353.1506220 149.6587421
## [541] 264.7860539 15.1844590 483.9278757 1670.2450886 1596.7183485
## [546] 40.4050539 39.8418414 198.3286842 2741.2644856 157.6757129
## [551] 424.8457220 203.7963264 786.5737237 1327.8842484 2225.9539756
## [556] 1543.4896610 1035.0731127 1256.0932999 784.7683623 80.8552890
## [561] 627.9503070 501.0762205 71.0314638 411.6472192 301.9351726
## [566] 477.0886018 100.8813306 418.4413250 178.7471089 529.3817562
## [571] 224.0653855 350.3061484 2520.1200776 14.4253259 186.8330427
## [576] 710.6726756 878.3616172 519.4732138 36.6358622 318.7625215
## [581] 1974.9052626 14.4912887 42.3368746 1182.8663227 215.3837674
## [586] 88.3355277 132.7925762 137.6184600 1684.1390840 156.4762059
## [591] 556.4157320 573.8533106 591.4226495 65.2604545 682.1672590
## [596] 525.0704153 412.8859234 61.8181555 175.4588459 76.8080493
## [601] 473.3616621 223.2574650 148.7665407 85.1825244 13.5908858
## [606] 1241.7147260 584.6076202 176.1005016 385.0030596 95.7768834
## [611] 63.8434074 399.7477974 592.8318947 265.9149412 513.6579731
## [616] 10.7925106 1217.9354196 27.3597573 187.9004480 176.6760521
## [621] 41.1471317 16.9619799 11.0967006 339.0555596 514.7306146
## [626] 106.6319465 887.5397741 553.8267959 570.9502422 237.3473435
## [631] 792.9138671 17.4776670 93.0693601 356.8714689 162.1762894
## [636] 243.6560895 205.3598603 478.4807940 182.3560120 234.9609083
## [641] 555.7201169 1447.7348571 91.4855177 1258.2541451 1933.3165762
## [646] 325.1365849 256.4070788 883.4458924 251.3254909 1168.8630943
## [651] 144.9582563 873.3211560 14.7429749 241.3340886 64.4437536
## [656] 142.2611827 82.1824835 12.0843919 493.0235430 385.2997273
## [661] 821.1428104 1137.2834434 80.6193652 226.5666237 114.8432596
## [666] 990.7082859 147.8591389 241.1457375 1094.4179490 22.2443014
## [671] 3.8048965 69.1734038 498.8909713 306.1013983 943.5849487
## [676] 1790.9483783 476.9619559 960.6751669 262.7660586 63.6476518
## [681] 1573.5050029 1686.4600367 12.3503378 27.4927348 55.3478592
## [686] 43.4760330 483.7865886 46.2864202 1647.3899967 92.4975602
## [691] 1013.2005941 89.0756934 2143.1592751 128.5887377 825.2743529
## [696] 2294.7453481 86.9672776 1089.6704208 38.1650985 48.1826779
## [701] 444.8423665 5.1054966 415.4363308 301.5743126 26.3331789
## [706] 185.1826143 234.0908283 392.8397237 317.0918955 314.0140257
## [711] 153.6841275 279.0491679 191.4544518 973.5026182 214.4474748
## [716] 210.4885024 901.5092225 275.4050002 481.0815914 372.3188424
## [721] 96.4218452 252.8739644 439.3348470 650.4380358 715.6576309
## [726] 1442.5748819 379.5786607 219.9656914 299.5555757 948.9598535
## [731] 79.9660347 859.2166500 362.9776252 1299.1037322 321.4884264
## [736] 722.7549929 437.5393063 8.0415062 114.9289384 582.3414549
## [741] 54.5948889 8.4457609 703.6552186 239.9546525 276.8442770
## [746] 1574.0376752 68.8217578 621.4675028 123.5073851 873.4369659
## [751] 906.5817315 695.8398819 456.9789036 221.4388813 728.9925498
## [756] 111.1402840 149.4438211 75.6376572 148.6956545 537.8224989
## [761] 815.2436483 1013.1449978 167.4805915 238.3885308 634.6957828
## [766] 646.0140650 249.5686763 212.3679270 151.8705043 52.9450397
## [771] 393.2486470 167.9955087 200.0896707 172.8115222 589.9223652
## [776] 68.7383188 740.4496579 530.1854606 1113.3180400 205.5905390
## [781] 188.2266621 559.3829695 745.1506229 1112.0203183 317.7661814
## [786] 229.7922825 623.2099579 702.2482823 64.8245667 53.1667693
## [791] 1657.8575372 448.0254774 1020.5018324 612.4879229 149.2086896
## [796] 768.2118713 67.2337981 661.7006422 1071.1552392 86.9518581
## [801] 188.1236855 189.1216664 1872.4170735 1047.5528468 112.1519348
## [806] 541.8141647 468.9408983 236.0941889 20.3174071 560.3416590
## [811] 136.1711377 623.7274054 349.3184017 17.0010764 231.4889987
## [816] 912.6052325 265.2777764 367.6136604 123.4484217 72.1254342
## [821] 543.9616958 207.7813496 984.6759932 910.3406248 398.1188046
## [826] 1279.4201811 25.2662284 270.1107683 1042.5441421 748.9666466
## [831] 76.1757996 149.2657135 216.2246932 425.6160883 234.9190095
## [836] 370.8864092 66.4104412 1108.6415657 79.5945211 181.8698531
## [841] 13.9703605 391.1260548 283.2306474 115.5936841 115.6951265
## [846] 144.7240852 159.8319981 689.6582604 106.7868680 1217.0890429
## [851] 864.9003198 172.1481858 359.8668277 191.1007343 628.7508914
## [856] 283.2048354 291.4025565 85.0604927 152.7530984 911.1989494
## [861] 243.6090037 387.9506937 4.5173402 331.6739472 177.7963182
## [866] 549.1911005 205.0515719 902.9948851 180.2079182 76.9672387
## [871] 850.7580357 284.7421989 1578.7312127 980.4279534 567.3413924
## [876] 21.8967604 266.0621679 974.1528360 867.6861743 174.4438104
## [881] 66.2887160 151.5835666 1099.2648071 112.9188238 270.4903942
## [886] 506.9843046 66.9499732 1088.8623213 7.0336957 99.2737142
## [891] 293.2937255 695.7035064 233.1041750 536.7980579 267.0303637
## [896] 292.0360554 1118.9465997 636.1993910 118.0259869 669.3842988
## [901] 209.7575001 625.1819732 373.6478016 25.5925672 71.9662082
## [906] 24.0466273 312.5867681 314.3220057 1338.3108442 843.8193434
## [911] 280.6682230 232.2385197 311.9517255 8.7673895 1383.1986700
## [916] 550.5297701 425.1725743 101.5214981 1093.7026776 281.9983745
## [921] 1123.9569960 590.0816580 46.7183141 95.0823649 407.3198424
## [926] 210.1192619 590.4730200 455.1640036 34.4307847 393.5353022
## [931] 6.9945799 707.3256976 592.7232066 1198.7247658 509.5665194
## [936] 261.2314443 1981.7699295 134.0216286 1873.6642179 1521.9288002
## [941] 108.6352593 737.9418703 1373.6266726 341.2013559 182.8723375
## [946] 922.6513337 177.7163375 93.9798399 774.8627811 410.6925945
## [951] 91.2519668 1720.9695726 321.0476732 75.7499153 863.9229581
## [956] 812.1144464 813.3038580 2071.4270201 1002.6300996 17.3299151
## [961] 940.5687507 840.8213136 1034.1977439 1116.7433494 19.4955816
## [966] 114.0441438 618.7543482 716.5475199 354.2025596 36.7490852
## [971] 1944.8365000 50.4740555 697.3631512 471.7957112 399.8110056
## [976] 478.3880965 2082.5463327 60.5892004 291.0283464 1338.3914762
## [981] 103.1774441 319.5695642 62.7783749 797.6287603 316.9056925
## [986] 95.2582597 1855.6567675 142.4062345 0.1738922 843.9561044
## [991] 841.8753013 412.7481490 338.2721380 1250.8615711 471.5915634
## [996] 814.1580429 599.9840684 193.6832722 478.6810227 161.9315492## B) Probabilidad simulada (que dure más de 700 horas)
prob_simulada <- mean(vidas > 700)
prob_simulada## [1] 0.246## D) Histograma de la simulación (forzando salida gráfica)
hist(vidas,
breaks = 30,
col = "lightgreen",
border = "white",
main = "Distribución de Vida Útil de 1000 Componentes",
xlab = "Horas de duración",
ylab = "Frecuencia")
- 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.
A) Simulación
defectuosos <- rbinom(100, size = 50, prob = 0.05)
defectuosos # número de defectuosos en cada lote## [1] 2 4 3 1 5 4 2 2 1 3 3 2 5 4 0 1 5 1 1 3 2 5 2 1 1 2 0 4 2 2 0 3 2 3 1 2 2
## [38] 3 3 2 3 2 2 0 2 2 1 3 4 3 2 0 1 3 3 1 0 2 2 1 2 5 1 0 0 0 2 4 2 1 3 1 5 3
## [75] 1 4 0 3 0 1 2 0 3 3 5 3 0 3 2 1 2 2 1 1 1 1 3 4 4 5## B) Número promedio de productos defectuosos por lote
mean(defectuosos)## [1] 2.15## C) Gráfico de barras
barplot(table(defectuosos),
col = "orange",
main = "Defectuosos por lote (100 lotes de 50 productos)",
xlab = "Número de defectuosos en el lote",
ylab = "Frecuencia")
- 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. A) Simulación
demanda <- rnorm(365, mean = 100, sd = 15) # Demanda diaria en un año
demanda## [1] 100.28983 102.79970 127.75186 106.02341 109.69908 84.76911 81.46243
## [8] 81.28661 80.03558 108.31396 86.61160 109.58806 93.66619 86.06655
## [15] 117.70104 100.56382 116.82488 103.79256 119.64843 90.39857 71.74308
## [22] 108.58105 91.81950 89.10877 87.50775 119.80683 105.48707 88.77321
## [29] 70.45571 92.22193 92.88585 102.38579 114.21996 95.28006 129.01955
## [36] 101.50505 120.31895 96.48714 95.80054 91.49542 90.83439 81.96434
## [43] 116.74247 94.76382 78.32739 74.14080 109.83616 121.02456 78.94540
## [50] 105.23070 74.14123 98.72705 105.91901 101.79191 96.09203 91.42826
## [57] 141.89413 116.76770 116.02330 117.31843 84.28757 119.27212 107.81200
## [64] 112.40790 93.97573 74.27946 91.38957 133.68842 117.41951 91.43365
## [71] 100.55957 130.93689 105.55996 110.16103 86.38697 105.38084 94.14734
## [78] 87.43917 97.86039 100.03043 98.05146 92.94454 103.31625 100.02041
## [85] 73.14952 94.00429 114.22534 107.52584 88.10242 106.16126 82.89512
## [92] 94.64186 89.84587 94.55031 91.01577 86.17510 113.13861 105.15465
## [99] 103.73876 104.47904 106.09843 115.13735 77.74289 102.18003 107.73471
## [106] 132.52761 90.43191 103.76374 80.94564 98.53908 88.47368 68.78229
## [113] 85.48949 96.24129 96.57206 84.85961 120.03578 108.27717 99.62970
## [120] 103.15461 93.48424 90.77822 114.52383 108.48399 106.13960 93.04526
## [127] 79.04840 112.41680 101.36648 121.12826 89.05915 79.40978 98.98622
## [134] 116.67792 110.88962 87.41180 110.72479 95.68109 106.41715 88.39367
## [141] 103.51162 92.96052 110.82509 91.58518 108.32036 91.63156 105.38477
## [148] 130.86336 90.26104 112.91164 93.32720 94.12862 113.36684 82.52749
## [155] 107.30630 70.36984 95.91657 104.35485 113.75508 82.80055 85.77997
## [162] 102.93041 78.53529 96.79433 135.06089 77.51821 115.78718 133.35914
## [169] 96.54323 66.24276 105.74488 78.65451 91.09283 68.69912 84.42007
## [176] 114.93036 104.54103 88.53754 111.76589 80.47370 78.93492 81.29061
## [183] 100.95692 97.44958 105.55546 86.82114 111.27011 77.95331 86.83706
## [190] 117.21459 108.67028 91.33528 108.73879 88.82321 83.06835 100.19525
## [197] 100.67167 80.80460 121.32024 99.82183 100.13017 96.70451 92.28148
## [204] 109.36168 97.25780 108.10037 114.11516 83.75934 87.34492 102.87578
## [211] 99.59954 119.19467 101.80996 96.79363 97.65356 95.61304 89.57832
## [218] 92.22363 92.83391 105.74023 120.06824 77.42118 105.06236 128.04825
## [225] 105.49081 111.47068 97.96828 85.25010 116.21174 100.01990 91.22215
## [232] 88.74291 109.99353 96.58413 68.91548 97.85313 120.12351 136.89657
## [239] 109.88863 98.39329 87.81931 107.64804 127.39291 83.24566 89.94369
## [246] 111.08283 109.60153 83.88229 97.55831 104.12902 122.97738 100.45221
## [253] 89.66403 75.14353 102.27328 80.22542 71.09027 94.04983 99.71010
## [260] 103.58623 92.01499 128.97832 109.51065 79.83325 96.45286 117.72015
## [267] 98.57975 94.63078 100.01205 82.83715 103.47447 76.83636 112.42065
## [274] 100.06724 88.09030 90.63884 102.73242 101.08250 118.44548 95.20088
## [281] 109.57390 96.83136 103.66541 99.26729 120.03842 107.11733 106.73846
## [288] 78.80336 105.76301 117.31824 101.95666 117.79188 107.06574 91.35536
## [295] 111.70038 82.28650 83.19991 108.19643 106.77112 103.31547 120.48641
## [302] 110.64858 95.63188 87.74309 106.13341 105.65715 97.03757 72.07650
## [309] 100.63270 109.12241 92.22450 116.96397 108.71804 132.07458 79.79663
## [316] 103.94919 103.26848 90.98807 92.17183 114.52862 85.50340 103.75043
## [323] 81.73711 97.20032 96.79844 91.66457 122.74556 84.61790 103.30249
## [330] 108.38976 115.31400 100.17536 133.81288 92.97870 90.56273 100.22732
## [337] 84.29145 98.73043 103.66029 77.86944 96.25358 81.77114 107.03361
## [344] 87.74000 96.78638 91.10775 116.41036 125.42785 108.55831 75.34017
## [351] 113.28608 141.01113 110.65418 115.06029 111.06597 92.51749 83.51890
## [358] 111.11784 104.33595 117.06153 104.38249 89.26444 108.80027 104.62565
## [365] 106.83214## B) Probabilidad simulada de que la demanda supere 130 MW
prob_simulada <- mean(demanda > 130)
prob_simulada## [1] 0.03013699## D) Histograma de la simulación
hist(demanda,
breaks = 30,
col = "skyblue",
border = "white",
main = "Demanda diaria de energía en un año (365 días)",
xlab = "Demanda (MW)",
ylab = "Frecuencia")
- 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.
- Generar 1000 tiempos de vida del capacitor aplicando el método 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 teórica de la distribución exponencial.
- Calcular la probabilidad de que un capacitor dure menos de 940 horas usando la simulación.
Simulación
## A) Generar 1000 tiempos por transformada inversa
n <- 1000
beta <- 1000 # β = media (horas)
# Generamos U ~ Unif(0,1) y aplicamos la transformada inversa: X = -β * ln(U)
U <- runif(n)
vidas_cap <- -beta * log(U)
vidas_cap## [1] 741.910920 2156.280174 2112.751766 1218.118150 126.254646 66.469446
## [7] 2515.643026 2819.433695 315.774451 466.488632 14.916408 439.758797
## [13] 357.069864 583.523851 6.791628 35.035285 795.877304 192.010105
## [19] 9.472196 525.514468 3077.904278 299.488795 360.558127 249.349222
## [25] 1643.255726 1314.946762 130.079886 74.475790 2751.529673 129.976880
## [31] 932.864142 785.167310 5451.583161 728.073387 1596.242021 57.988429
## [37] 416.920141 626.888505 3755.548288 833.573322 26.457715 890.178356
## [43] 633.789935 40.406895 168.601423 255.807441 171.622898 1225.156341
## [49] 448.442961 642.464469 2199.749925 345.434266 80.370825 1089.919131
## [55] 1772.298263 173.024987 409.464724 1505.890140 1956.958378 1419.830594
## [61] 560.553885 1600.575424 3719.354186 302.053174 1749.217993 794.208951
## [67] 1552.593128 1442.699731 958.393980 570.692313 105.615947 672.764128
## [73] 92.530246 547.508060 52.483480 2213.469370 1508.968193 419.185394
## [79] 2775.917618 276.329714 276.028559 1805.674411 28.977226 439.816286
## [85] 496.920313 1252.407437 2979.626692 12.590275 1395.778651 830.878939
## [91] 9.378935 190.166312 1118.139510 1496.250178 676.462434 500.693167
## [97] 400.902087 670.004503 1303.362345 839.725835 785.154407 1279.186775
## [103] 1456.710635 996.943166 516.380082 1034.788181 856.843877 844.252113
## [109] 170.571923 173.827130 373.018362 1144.462870 86.646423 1882.652374
## [115] 97.558818 741.915908 91.702900 1234.259993 117.377224 161.124052
## [121] 544.472168 759.698630 1809.978558 5743.739103 669.760651 115.575966
## [127] 181.209371 808.239765 84.631454 22.601411 3979.185220 1002.642881
## [133] 252.318540 674.896095 381.855752 176.850417 1660.226281 320.341993
## [139] 469.987564 246.822441 2001.476358 80.357525 1646.195224 759.202162
## [145] 1264.844411 1015.252182 451.182973 247.007620 1265.797263 639.047329
## [151] 1242.949634 782.839128 55.671686 405.140730 1839.237069 337.299766
## [157] 335.146629 1333.008647 210.936814 306.441245 52.195927 77.590711
## [163] 10.577141 1239.252464 1142.048352 1513.897146 360.470880 633.511112
## [169] 98.705133 279.242146 1736.958861 1213.170574 43.628602 1106.850023
## [175] 3838.275038 416.501826 1446.290483 362.702284 702.515928 666.078593
## [181] 1781.689149 396.043880 1309.546441 1280.606976 220.977566 267.737593
## [187] 892.938782 635.301032 1077.497784 304.077563 2563.532351 1918.456319
## [193] 3.513339 1513.198325 2060.006533 208.397741 57.447459 171.275679
## [199] 113.666376 3253.669639 714.051390 350.866289 606.813563 1951.493382
## [205] 220.165887 1104.656966 432.244738 578.087518 1273.469202 9.181017
## [211] 250.417493 2415.073439 476.339683 521.132633 1181.466093 141.818403
## [217] 284.932574 2861.255260 881.190222 19.060883 463.499025 634.295019
## [223] 1337.920505 1428.613019 908.961169 204.558879 34.390695 497.214665
## [229] 576.396660 1050.734794 590.780854 749.504960 525.099845 745.488050
## [235] 145.304466 63.107932 267.032942 386.107264 233.490875 1033.258592
## [241] 514.172948 1902.220193 421.092850 939.657850 2152.619854 441.544185
## [247] 1531.883063 377.733684 703.858892 180.924232 497.682395 256.316680
## [253] 1621.283397 398.387507 740.763324 2131.605263 283.741631 2379.201914
## [259] 490.396615 230.198905 427.875151 1029.349590 1286.242163 555.560887
## [265] 171.825956 331.936552 445.649462 381.036165 823.085770 271.782165
## [271] 265.779961 1495.131912 677.533479 1937.841244 227.862268 765.114659
## [277] 2681.138466 1331.730355 912.824945 1369.116022 446.275257 3523.848222
## [283] 3031.844011 300.824472 598.577022 71.958696 656.625733 490.003907
## [289] 1326.872897 687.996929 314.799873 520.850126 225.553802 74.931756
## [295] 975.752927 1290.230454 3669.796688 1754.872694 667.692807 225.386303
## [301] 309.314897 522.599520 1135.153880 1656.687352 2186.275115 2991.491652
## [307] 955.579594 2344.413137 1026.138420 342.023653 126.222320 520.579734
## [313] 75.290079 2654.099151 439.004704 473.345149 227.490620 585.439908
## [319] 502.091940 488.440325 638.270587 1877.456316 284.672665 422.748883
## [325] 44.557147 35.822586 914.619774 16.461888 754.321349 228.454676
## [331] 242.276107 382.265150 344.360318 2099.089194 962.765372 1662.140284
## [337] 4222.165499 1323.927974 936.871829 1311.526668 574.919035 873.464171
## [343] 563.534364 1009.041748 179.754306 1801.422183 841.649357 477.376021
## [349] 6.964760 847.351307 628.899883 2928.074819 54.419978 1275.920479
## [355] 389.980797 405.545520 795.063055 128.179816 414.098518 826.142120
## [361] 545.153839 1426.134168 808.344529 103.636863 382.836361 198.561074
## [367] 1709.171487 2239.466443 721.774342 723.877983 73.910500 1662.333175
## [373] 2833.372945 16.829484 2079.811777 135.987929 686.116734 491.516510
## [379] 449.414965 148.422633 14.279597 1907.316115 142.617525 2756.414577
## [385] 3080.885696 1047.072185 121.437127 319.761328 530.587975 720.750779
## [391] 1489.241042 5331.757952 239.252169 1606.366282 605.410351 898.705434
## [397] 2009.182794 638.876212 996.229084 850.581752 933.311874 994.079472
## [403] 668.353977 2347.726485 184.089784 921.041248 46.782369 74.104533
## [409] 430.735703 460.982233 132.311091 1179.412510 2365.329818 157.002035
## [415] 654.448419 1828.106685 467.311491 62.139890 333.499651 194.064098
## [421] 1845.998074 395.444150 3419.236906 71.256303 1299.703246 85.246592
## [427] 2189.629738 473.008195 1435.902266 575.187541 2632.981257 608.087596
## [433] 2634.844723 282.197633 979.575971 2163.588460 1044.222008 1024.537782
## [439] 928.405695 1747.363580 371.761669 236.957615 600.011802 698.259713
## [445] 1161.423944 593.718879 673.401751 1083.240196 818.382869 892.199338
## [451] 263.323096 5.911788 155.423228 433.863865 1225.743289 186.311518
## [457] 246.263327 18.588922 284.174773 413.620359 827.632976 2315.668891
## [463] 4301.772166 307.360504 1898.541478 228.171225 5111.301330 666.077916
## [469] 791.431730 1066.402628 1073.621271 641.176832 299.683773 365.738316
## [475] 68.887468 1006.167944 1454.619526 141.327469 183.982809 333.163563
## [481] 19.227990 161.774991 157.586315 110.110134 1791.608503 732.763049
## [487] 172.620338 749.922166 977.198934 118.295626 2064.487151 222.126816
## [493] 2390.048683 486.004619 117.355652 462.777827 31.819895 557.569324
## [499] 1969.917477 426.286595 2950.959080 114.149633 574.602573 1951.809198
## [505] 1036.995898 1094.468099 141.267304 3006.921829 2890.398015 822.451467
## [511] 705.006631 3554.767831 2145.217764 1392.568826 691.967957 3660.569547
## [517] 723.576863 1109.717755 729.445232 381.022927 577.151139 1397.734357
## [523] 174.740761 1697.703519 253.533142 89.510032 1139.650375 732.174452
## [529] 671.715596 106.580392 1153.817641 650.634503 215.779059 11.051532
## [535] 1318.770523 47.689236 66.977100 981.622445 262.445064 1901.009977
## [541] 516.923012 114.203200 2397.517795 649.178130 739.060294 301.212712
## [547] 646.289852 511.752758 187.769067 2071.365975 804.432128 100.688916
## [553] 88.580589 103.188787 6962.661745 355.334102 56.765913 2516.591129
## [559] 1039.449231 622.419131 1879.517877 10.782798 13.401208 997.810018
## [565] 228.770807 2207.679546 543.331690 1780.166728 297.995603 1396.798261
## [571] 1071.020292 392.961398 257.528844 21.101297 729.407277 2387.056181
## [577] 269.009183 235.225544 1819.738189 1964.934783 316.447289 1332.096342
## [583] 72.797313 2092.086247 1128.148408 406.424816 1467.820941 18.970963
## [589] 991.250057 458.391040 2340.381469 1660.687381 885.191707 438.644016
## [595] 143.587968 673.713798 558.169429 1135.961277 303.147113 556.504314
## [601] 2633.725563 482.042138 1368.567060 1476.611906 817.326317 2209.495626
## [607] 159.814157 1274.644224 1069.740869 846.249802 5674.922638 235.786443
## [613] 2028.634741 590.963090 1567.645128 162.745531 187.566458 243.705923
## [619] 23.778700 800.664997 796.065535 1667.608087 239.298113 876.033724
## [625] 1439.788493 243.423738 1062.062229 563.722644 601.630523 123.902110
## [631] 637.488637 549.118155 742.109477 733.929583 648.453341 874.578148
## [637] 5301.994577 753.146136 388.205850 169.635997 869.865372 808.883096
## [643] 647.015588 3939.222472 2035.425991 744.786181 405.224573 2466.385777
## [649] 2718.091444 241.947580 206.996978 1160.935169 1045.747205 480.069835
## [655] 23.869590 603.551520 279.932644 252.559201 165.493883 2230.584395
## [661] 1373.038718 1213.807598 1276.412014 2144.712059 1533.612457 1433.888889
## [667] 1025.842673 1502.713601 1659.283535 1244.525157 3224.364738 202.879760
## [673] 243.771686 1618.957313 1044.262594 10.695844 91.344753 18.416057
## [679] 334.170777 87.669479 1928.319232 648.128650 1109.900447 231.141563
## [685] 268.435536 463.484179 417.103900 60.912272 639.323370 4549.331121
## [691] 1895.167988 19.183068 677.687974 246.258370 1215.988034 1525.918503
## [697] 3.658216 788.973610 766.034907 2895.252459 404.599915 29.162699
## [703] 106.738973 679.902078 220.685979 63.639909 1044.067914 2051.162080
## [709] 498.949875 999.121467 529.906154 225.914622 2310.961340 920.485995
## [715] 2149.964466 473.347839 70.372344 390.882503 24.467610 110.284106
## [721] 1207.253445 4013.018257 118.553710 3206.294041 667.130045 216.852595
## [727] 1088.229963 874.857630 1173.216505 1464.400313 881.139754 3555.497374
## [733] 1334.817954 1470.119516 700.135106 1519.150663 620.461194 1563.714523
## [739] 3523.619538 1610.045366 490.346842 794.639494 4874.643396 681.089556
## [745] 253.839302 462.857414 542.643123 1331.688220 842.986581 32.192731
## [751] 1060.488026 941.097379 267.895894 37.459820 766.204989 499.121177
## [757] 1226.107443 782.159807 191.809500 4172.375822 224.559288 168.200645
## [763] 1071.231994 172.760322 1656.960350 2001.450257 43.579175 1820.395712
## [769] 373.179040 2664.054357 572.935311 116.964183 437.384363 1242.482214
## [775] 648.065937 1737.682840 381.290959 878.192846 2439.577687 701.031936
## [781] 941.211929 2381.197405 809.028876 471.216445 565.031018 218.995452
## [787] 1789.441145 653.154449 2623.116513 910.478964 89.853126 270.138607
## [793] 336.943733 430.616609 1913.911658 1223.554969 1534.157490 199.560126
## [799] 122.167094 53.496132 93.629509 3024.580141 1006.002338 345.028653
## [805] 326.808481 488.931597 223.294781 87.776269 225.039292 293.093584
## [811] 758.468064 1794.929724 493.283235 201.273154 1173.293973 3245.332002
## [817] 217.156889 655.269844 727.932552 1326.165616 125.161459 2064.620335
## [823] 1519.321945 3111.676688 122.224634 338.921835 1013.397452 777.291390
## [829] 181.139563 1628.997164 1362.823433 3008.552447 951.349689 1179.607892
## [835] 2095.007082 523.130013 138.325751 452.318408 2520.753861 844.706569
## [841] 27.070398 67.536354 1341.711302 525.156986 636.315247 270.551625
## [847] 870.633960 2370.467790 615.360310 4445.459068 14.491407 439.947090
## [853] 686.253874 668.917101 2457.878776 1039.640165 1195.361582 1225.602207
## [859] 320.731369 1395.905604 1125.903723 198.175789 791.352146 567.250912
## [865] 682.672915 8.828216 518.817488 308.083888 2447.016226 2292.349221
## [871] 3716.008933 448.697316 167.764777 23.438737 1043.372794 401.442442
## [877] 157.198782 1351.371824 98.031821 479.306179 2776.632203 1238.348238
## [883] 340.991175 1833.114738 447.014288 2555.231909 36.104567 1483.701702
## [889] 1905.270442 169.525200 263.195550 313.108651 954.111231 244.031232
## [895] 673.773383 3567.727609 2426.497921 17.256132 3751.462046 300.488120
## [901] 301.948752 312.111901 4019.088030 84.069862 681.397791 2400.333719
## [907] 508.775580 949.788262 1207.867146 1138.541279 287.729654 272.281842
## [913] 273.749291 743.408440 184.347793 486.506024 274.175232 2529.122329
## [919] 3672.742412 1189.406241 298.283176 1082.409586 438.068682 292.306298
## [925] 2336.781883 173.503593 507.319818 460.984292 1652.157230 4177.870241
## [931] 140.499282 1244.405441 944.856620 48.865970 968.807580 1539.146954
## [937] 83.013159 158.630556 605.636858 481.280764 1761.161346 16.484129
## [943] 551.230948 87.859510 89.979010 469.756888 278.538725 2258.178865
## [949] 1204.396143 738.645006 539.747345 1186.236183 154.227836 1503.301151
## [955] 481.947710 345.034582 1989.727663 388.436886 508.804915 478.906842
## [961] 603.616970 800.222247 677.693073 975.148156 1112.109889 2010.322193
## [967] 186.626940 2831.516229 1828.173342 1501.108279 631.780161 2263.733397
## [973] 604.219345 1494.515634 138.275266 1814.441597 1122.036825 546.298611
## [979] 1210.497626 650.503405 806.845535 3798.292918 90.707966 311.309743
## [985] 1796.133958 1586.340998 768.343989 544.243732 975.265852 539.524029
## [991] 753.701752 2083.734705 1766.130099 1144.539018 1379.769352 2264.393985
## [997] 761.019882 2220.842914 4.127011 430.528374## B) Estimar media y varianza (muestrales)
media_muestral <- mean(vidas_cap)
var_muestral <- var(vidas_cap)
# Mostrar resultados
cat("Media muestral:", media_muestral, "\n")## Media muestral: 960.5053cat("Varianza muestral:", var_muestral, "\n\n")## Varianza muestral: 922807.8## C) Histograma con densidad teórica sobrepuesta
hist(vidas_cap,
breaks = 40,
col = "limegreen",
probability = TRUE, # para que el hist muestre densidad
main = "Histograma de tiempos de vida (1000) y densidad teórica",
xlab = "Horas de vida",
ylab = "Densidad",
border = "grey")
#densidad teórica de la exponencial: f(x) = (1/β) * exp(-x/β), x >= 0
xseq <- seq(0, max(vidas_cap)*0.95, length.out = 400)
lines(xseq, dexp(xseq, rate = 1/beta),col="navyblue", lwd = 2)
## D) Probabilidad simulada de que dure menos de 940 horas
prob_simulada <- mean(vidas_cap < 940)
prob_simulada## [1] 0.628