Tarea2_Estadistica2
Alexis Ovalle
2026-08-07
1. Genere N = 100 muestras aleatorias de tama˜no n = 10 de las siguientes distribuciones:
Se utilizara r, esto para tener valores aleatorios en cada funcion.
Para la distriucion uniforme contunua
matriz_uniforme <- matrix(runif(cantidad_elementos, 1, 100), N, n)
print(matriz_uniforme)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 51.051785 22.719702 36.478546 90.094297 3.098513 50.707931 73.160813
## [2,] 18.987690 2.516076 11.707549 72.353832 82.754370 41.198551 71.154298
## [3,] 61.440642 58.620843 40.075331 5.320384 5.197841 91.039453 24.560314
## [4,] 60.649224 7.620597 48.026845 46.798357 49.307227 10.576724 53.133820
## [5,] 72.988244 94.862398 68.023403 56.307448 25.738858 70.047864 42.216464
## [6,] 59.810639 2.540682 17.548905 1.908428 36.737682 8.987286 73.976422
## [7,] 15.551010 61.286028 73.103784 40.966366 54.943750 10.162585 67.315607
## [8,] 39.855711 86.259216 49.063189 97.920249 51.236954 68.897693 41.095164
## [9,] 99.920230 30.668363 3.563404 30.273273 48.250254 12.492702 35.143630
## [10,] 53.655358 32.277590 86.341648 85.716850 82.228081 16.127605 37.482493
## [11,] 10.584083 91.942390 18.439716 72.156452 9.859815 66.267538 93.146385
## [12,] 52.327380 85.224539 61.902025 11.144333 2.315974 67.655318 66.574384
## [13,] 99.382454 86.568810 92.694903 26.428870 65.417906 47.711294 72.322680
## [14,] 17.310820 77.664940 46.335162 72.037011 7.096773 44.312539 88.946469
## [15,] 69.512645 63.556412 43.616605 20.980089 65.905298 51.466016 83.675534
## [16,] 77.922228 87.925925 67.590434 81.270081 66.591018 95.663741 67.522702
## [17,] 45.635375 53.631066 70.286157 14.788628 28.274466 9.766289 25.708691
## [18,] 40.277198 1.443502 96.038567 65.178801 86.854678 83.565302 16.000053
## [19,] 26.275613 79.105814 13.445105 27.448146 59.844895 19.751456 87.460206
## [20,] 67.131902 93.055835 75.344735 87.128991 59.706531 12.897708 72.482357
## [21,] 79.523300 3.126820 21.115207 74.564863 75.647220 13.491107 83.422755
## [22,] 6.008607 23.896853 3.059391 48.648717 76.362838 3.089798 77.311621
## [23,] 2.244278 88.482503 70.762204 35.870544 81.991811 93.884318 71.251921
## [24,] 93.016293 67.493563 87.389465 65.224952 88.905124 78.358219 81.826726
## [25,] 75.700027 5.617544 39.833068 48.339788 43.458914 24.593413 88.003795
## [26,] 13.382145 31.054213 1.998362 62.746320 41.281774 12.803827 14.242351
## [27,] 91.245015 35.611885 82.716695 66.754747 72.150904 74.688559 54.908068
## [28,] 2.938906 75.073058 65.038221 50.750923 96.757677 86.444755 24.198854
## [29,] 68.156915 57.985860 13.047830 84.749457 21.605516 49.063400 25.068375
## [30,] 17.205924 47.007886 49.459225 74.156882 95.377901 96.741538 16.463068
## [31,] 56.310308 50.319261 21.790160 72.100419 23.918635 9.582245 19.938468
## [32,] 46.077350 50.708536 63.616820 79.414267 56.111628 9.812649 36.430184
## [33,] 16.313492 77.149618 43.085826 37.670644 45.170768 58.094196 21.346875
## [34,] 34.855369 40.359080 94.043336 78.409394 36.643584 91.969058 70.513338
## [35,] 99.007736 40.303294 72.555320 4.327927 9.499507 76.499089 18.732246
## [36,] 73.362294 15.106614 39.154073 65.483641 89.310212 99.270093 43.421853
## [37,] 14.444500 85.184982 34.472928 79.386194 72.671144 88.189513 41.427457
## [38,] 49.321954 50.579839 99.166010 90.514811 99.598733 65.261800 99.199745
## [39,] 78.327052 26.821782 59.332448 63.162668 34.312561 94.545332 32.854818
## [40,] 62.177758 17.097319 96.241989 8.893910 97.400643 94.807744 94.164231
## [41,] 58.737901 49.519881 73.660754 16.549420 35.145963 56.938934 89.841255
## [42,] 75.210849 12.415510 91.540534 10.437657 31.597503 22.084227 77.267498
## [43,] 81.452135 92.780166 75.009011 43.013701 17.744144 7.942341 52.878211
## [44,] 38.180134 54.166807 62.691928 34.597169 29.165968 64.971875 95.142435
## [45,] 77.509298 40.822489 35.230116 44.062129 22.080403 6.816721 6.497682
## [46,] 89.318304 68.089265 50.736451 90.761449 97.538478 82.175303 55.830049
## [47,] 11.335409 38.590967 4.065227 51.121421 73.393189 69.041720 13.518366
## [48,] 96.555441 53.946345 97.532214 12.259968 23.262899 22.610789 92.102674
## [49,] 74.442552 32.144030 40.800528 65.863531 59.185982 58.263066 98.120970
## [50,] 99.111495 23.077089 57.929676 94.744292 53.214151 78.907710 11.092590
## [51,] 34.778629 62.993994 17.201321 61.977899 82.745443 2.177100 27.840324
## [52,] 13.928803 74.115946 81.819629 82.424234 53.716702 28.126463 46.296777
## [53,] 85.623384 38.700581 80.916584 1.232379 79.402965 39.351778 81.766283
## [54,] 31.012258 11.019945 65.754911 12.438376 95.850857 4.932746 16.227033
## [55,] 7.112994 33.192012 29.575294 48.531927 98.258286 31.784165 78.592300
## [56,] 78.580590 18.734041 93.024866 2.334766 86.384063 67.098726 31.843303
## [57,] 22.056014 56.427847 92.678416 49.158207 66.594323 35.067533 12.430997
## [58,] 54.645685 49.355678 83.753450 26.700169 90.803934 46.206052 76.405198
## [59,] 44.114177 58.928513 37.353488 48.781206 62.329367 66.261453 56.933385
## [60,] 29.081688 89.928410 95.997287 48.792785 13.245679 10.601620 92.643056
## [61,] 21.595205 57.879330 94.940796 49.290450 87.960214 87.649825 19.373457
## [62,] 90.357418 24.083547 72.850661 8.484770 66.441329 68.119928 70.824339
## [63,] 90.676583 95.549438 40.422007 42.131779 38.812927 94.729122 86.017618
## [64,] 19.516469 41.723116 19.459993 35.587401 72.058293 31.542274 79.049349
## [65,] 78.792417 54.429736 99.646526 49.374715 96.533141 83.913703 36.246614
## [66,] 6.368176 8.255972 58.636242 43.997927 97.502052 51.057861 75.464731
## [67,] 46.123830 67.961561 44.171799 35.199406 21.751518 15.025704 73.806158
## [68,] 23.313541 93.019750 66.806869 54.231184 64.411942 73.065494 6.919271
## [69,] 72.175745 69.736463 8.943875 10.766163 23.683094 95.879478 74.428589
## [70,] 49.141990 8.215830 90.287525 48.013397 12.090771 41.685028 48.395754
## [71,] 5.722678 12.306714 94.935502 80.143295 70.367118 20.831308 72.485001
## [72,] 54.525273 67.497561 14.079893 52.782298 35.911184 20.894019 54.927907
## [73,] 70.019731 61.893936 7.833412 13.806584 78.646682 49.210152 70.784185
## [74,] 40.470567 15.094538 29.734039 49.920108 83.184673 65.940524 70.363851
## [75,] 96.942141 39.624591 18.966743 10.630306 82.855096 80.127927 85.242042
## [76,] 79.266045 38.948046 54.833517 79.799502 51.369968 17.313957 98.313397
## [77,] 17.351341 71.671894 41.631434 5.456048 9.013780 39.355490 71.628830
## [78,] 93.935026 91.332798 94.210947 62.213410 8.583312 70.091683 96.011132
## [79,] 12.350006 7.304909 35.417542 20.313300 23.942493 65.055049 97.766086
## [80,] 93.557228 20.153265 44.494777 38.848503 2.784706 9.584382 77.640390
## [81,] 3.868234 74.746391 45.727038 36.603015 68.048170 57.183796 51.946697
## [82,] 84.830361 64.736978 12.589217 26.418367 22.964234 88.533155 29.008089
## [83,] 82.442434 63.086581 70.564348 51.492966 78.694313 25.050112 92.459447
## [84,] 19.750377 39.090508 33.491056 52.660711 45.851609 29.705964 6.141405
## [85,] 53.959918 59.988265 7.545322 72.599123 78.117034 32.043194 26.589314
## [86,] 44.041238 39.384125 66.944834 29.316780 49.085989 46.960848 19.872651
## [87,] 55.217422 30.589319 37.674342 31.171048 96.799926 74.362027 4.989070
## [88,] 50.479695 73.464828 70.721624 5.417739 17.397658 3.282753 1.006574
## [89,] 76.089303 66.462559 1.571221 76.407603 49.989126 72.777006 58.642113
## [90,] 90.094912 43.110427 1.764898 26.427937 15.260583 85.220683 79.312447
## [91,] 94.629410 73.585295 24.458360 4.386043 31.949598 7.983271 75.509723
## [92,] 36.894470 60.440030 98.746186 36.807183 48.118117 91.025879 50.616388
## [93,] 24.802677 98.110050 7.553051 18.586925 13.397054 83.433971 2.337626
## [94,] 26.084068 52.409289 38.979528 72.292945 14.578030 24.117077 7.927466
## [95,] 33.329616 28.787125 74.575938 68.990409 51.167118 29.631428 13.604824
## [96,] 49.008052 96.005396 19.431290 25.225566 79.035443 7.910309 99.484055
## [97,] 74.243955 50.045888 55.714515 99.109419 62.440916 71.516591 31.975818
## [98,] 66.091846 84.753250 49.569463 95.711055 63.856250 68.747933 64.894079
## [99,] 15.674741 23.108865 91.726775 53.748979 63.420162 71.488272 99.105853
## [100,] 17.707547 54.989309 72.307881 5.478196 41.944542 74.086887 20.714819
## [,8] [,9] [,10]
## [1,] 6.601218 14.676701 93.076710
## [2,] 95.732858 50.287077 36.277652
## [3,] 18.933045 37.445840 40.740648
## [4,] 89.924015 85.139539 64.170448
## [5,] 21.753543 7.685649 67.462225
## [6,] 65.024738 23.550075 1.450551
## [7,] 3.246893 61.157909 58.787470
## [8,] 77.899304 82.644759 7.907993
## [9,] 51.083761 13.014554 94.183471
## [10,] 38.087202 2.560346 39.926990
## [11,] 97.291201 57.596642 72.130421
## [12,] 97.169199 76.545648 5.023827
## [13,] 87.361875 30.903840 13.978429
## [14,] 85.767636 16.321091 33.893692
## [15,] 32.120847 14.303024 78.304836
## [16,] 57.945754 6.164159 81.103819
## [17,] 30.029891 15.120163 88.730163
## [18,] 71.794290 84.761448 24.067725
## [19,] 20.652050 85.935636 88.664215
## [20,] 33.512823 21.783236 1.152182
## [21,] 84.764122 78.671369 60.680954
## [22,] 98.642426 30.661129 27.299319
## [23,] 87.811905 56.179394 21.747454
## [24,] 38.183895 83.473122 94.525690
## [25,] 27.424609 2.654352 83.627479
## [26,] 55.268700 60.870136 35.959522
## [27,] 58.594282 8.293907 40.649712
## [28,] 49.841709 88.052522 86.077846
## [29,] 37.793541 9.989438 90.980898
## [30,] 18.399224 66.661058 76.685399
## [31,] 6.583339 87.165128 68.709327
## [32,] 80.072727 22.902735 29.869882
## [33,] 89.705588 84.037997 46.709979
## [34,] 26.652835 5.678543 12.837672
## [35,] 89.510205 90.297138 19.606342
## [36,] 4.989485 79.425423 12.605420
## [37,] 4.212850 43.790346 67.565839
## [38,] 2.658060 10.701303 88.336435
## [39,] 32.651820 38.363936 62.659935
## [40,] 76.224075 34.293087 63.779032
## [41,] 86.495167 52.954050 4.057215
## [42,] 78.035063 66.665608 89.302298
## [43,] 20.386635 76.700075 82.578727
## [44,] 36.064427 61.759024 69.701881
## [45,] 40.765362 74.149725 56.728779
## [46,] 39.090376 47.821023 10.860845
## [47,] 97.685503 16.253736 14.435880
## [48,] 96.451036 51.994247 78.933969
## [49,] 16.361920 81.636947 5.683416
## [50,] 69.901523 59.531306 45.601977
## [51,] 94.629289 39.217019 79.461087
## [52,] 56.434526 74.437788 64.483106
## [53,] 23.990691 26.660376 45.818142
## [54,] 27.133599 69.574865 23.380618
## [55,] 18.514028 1.737157 75.008306
## [56,] 39.768960 7.047260 68.499389
## [57,] 33.616103 12.185188 59.197393
## [58,] 24.296881 1.460334 17.142138
## [59,] 53.383671 28.384157 22.655552
## [60,] 9.959714 19.179319 17.515851
## [61,] 80.973817 44.226187 17.498812
## [62,] 22.193864 78.386513 65.704042
## [63,] 81.794780 34.954656 6.177122
## [64,] 15.348575 53.076724 60.256300
## [65,] 14.574381 95.566739 65.172870
## [66,] 48.411778 24.897130 35.294914
## [67,] 20.603724 21.074181 22.179769
## [68,] 32.583877 68.028571 35.518182
## [69,] 50.261441 87.330163 18.105544
## [70,] 31.412308 68.172026 40.218824
## [71,] 78.058120 9.985573 30.117472
## [72,] 34.745170 22.242057 78.566589
## [73,] 95.889563 45.407880 49.420118
## [74,] 48.386313 73.926281 48.303407
## [75,] 95.417244 29.531588 12.149983
## [76,] 25.958522 92.171932 89.434095
## [77,] 91.924241 35.832133 64.906359
## [78,] 10.146684 13.980522 10.740724
## [79,] 12.716232 21.664864 81.474347
## [80,] 43.400171 11.094354 63.146904
## [81,] 9.007300 88.613064 24.861062
## [82,] 63.757644 7.133549 44.018737
## [83,] 5.378408 13.342963 67.110567
## [84,] 18.376886 87.749461 89.934066
## [85,] 19.394120 22.579578 43.586414
## [86,] 91.895146 57.262696 19.264703
## [87,] 76.811410 76.448879 29.074114
## [88,] 10.803396 60.493967 43.914572
## [89,] 37.213233 22.860768 87.856598
## [90,] 11.679610 48.179281 65.278405
## [91,] 89.082600 74.204694 51.504495
## [92,] 55.592305 9.065133 15.212364
## [93,] 59.620515 16.865135 71.934556
## [94,] 45.202968 14.010920 76.873692
## [95,] 25.260417 97.483919 1.315329
## [96,] 81.166034 92.538973 29.071456
## [97,] 69.500836 2.007083 70.096347
## [98,] 12.006538 32.551079 22.124734
## [99,] 64.087001 73.661104 55.251226
## [100,] 23.093624 1.260188 46.554596Poisson
matriz_poisson <- matrix(rpois(cantidad_elementos, lambda = 50), N, n)
print(matriz_poisson)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 50 46 52 58 39 45 54 47 58 44
## [2,] 50 54 54 72 57 55 43 49 49 53
## [3,] 41 45 43 46 53 54 54 48 58 41
## [4,] 73 63 58 56 55 65 44 46 49 56
## [5,] 43 49 44 62 45 50 47 49 41 47
## [6,] 52 51 46 46 59 46 55 58 62 59
## [7,] 57 43 56 51 46 50 48 54 45 54
## [8,] 44 59 54 39 44 61 45 52 55 56
## [9,] 45 44 39 47 40 46 50 45 58 45
## [10,] 59 47 47 57 47 55 56 60 40 44
## [11,] 52 45 44 48 43 40 47 42 48 49
## [12,] 59 59 58 55 53 62 50 48 53 53
## [13,] 42 51 50 46 59 45 41 56 53 45
## [14,] 52 50 51 50 44 59 37 44 52 36
## [15,] 68 51 44 49 60 45 44 61 48 49
## [16,] 46 52 57 49 63 66 51 51 44 55
## [17,] 48 48 49 60 60 47 59 52 53 49
## [18,] 51 47 47 49 45 48 48 58 53 50
## [19,] 48 47 49 61 53 57 41 51 52 54
## [20,] 60 52 54 51 37 53 43 51 51 51
## [21,] 56 48 43 52 60 49 59 48 42 46
## [22,] 45 54 49 36 40 56 43 35 53 49
## [23,] 40 41 54 37 42 55 43 45 55 50
## [24,] 59 55 56 42 53 52 57 43 55 44
## [25,] 44 48 53 45 45 50 45 52 44 45
## [26,] 42 65 51 47 68 65 43 48 63 46
## [27,] 59 45 50 56 51 43 48 50 44 43
## [28,] 52 49 37 60 65 55 47 47 38 50
## [29,] 49 45 52 54 60 56 44 39 49 56
## [30,] 45 43 64 68 40 44 51 41 52 43
## [31,] 61 46 47 52 45 48 51 60 62 56
## [32,] 47 48 53 52 53 54 32 65 50 62
## [33,] 56 36 52 43 60 46 52 61 42 47
## [34,] 41 56 45 50 51 59 40 49 71 52
## [35,] 54 46 45 46 45 38 50 60 50 52
## [36,] 57 59 49 65 53 64 45 45 51 45
## [37,] 36 40 41 44 49 48 53 36 50 43
## [38,] 48 33 39 59 32 53 49 59 44 23
## [39,] 48 51 50 49 57 45 46 47 52 36
## [40,] 52 49 65 55 50 44 37 47 43 38
## [41,] 53 55 60 49 56 46 55 65 49 41
## [42,] 45 52 41 46 51 48 37 56 46 37
## [43,] 42 48 51 47 55 42 65 52 42 40
## [44,] 44 40 44 54 56 46 42 46 48 37
## [45,] 49 55 39 45 50 56 56 57 41 47
## [46,] 43 48 44 45 52 54 47 49 46 48
## [47,] 53 51 56 43 51 51 45 47 52 41
## [48,] 43 43 52 42 48 52 52 46 44 60
## [49,] 58 46 49 49 54 59 59 53 71 58
## [50,] 61 50 49 56 55 37 65 50 39 59
## [51,] 45 45 59 52 43 46 44 61 44 51
## [52,] 56 45 50 43 43 52 49 40 42 39
## [53,] 50 46 53 51 52 55 60 55 53 45
## [54,] 62 52 52 59 48 50 45 50 50 65
## [55,] 45 44 40 56 51 57 59 40 54 62
## [56,] 48 39 46 37 46 47 53 48 42 47
## [57,] 54 48 49 50 39 45 53 47 49 48
## [58,] 41 45 50 59 49 47 52 43 48 26
## [59,] 44 64 45 43 62 65 45 39 49 55
## [60,] 48 42 51 60 47 31 46 42 46 49
## [61,] 64 59 41 45 53 43 51 55 46 48
## [62,] 42 44 38 47 48 47 45 56 44 62
## [63,] 67 40 54 59 52 47 55 31 51 52
## [64,] 55 48 56 33 42 48 55 37 46 45
## [65,] 48 52 48 44 60 60 53 46 57 49
## [66,] 59 38 39 48 47 37 54 53 65 42
## [67,] 46 46 46 55 55 51 52 43 59 42
## [68,] 52 41 40 57 55 47 56 57 56 44
## [69,] 67 46 58 61 53 55 56 48 49 43
## [70,] 55 55 50 61 57 36 47 54 46 44
## [71,] 54 46 54 54 60 40 45 43 50 60
## [72,] 50 44 55 40 53 45 47 49 54 43
## [73,] 55 55 40 59 45 48 54 63 48 51
## [74,] 55 59 50 43 38 55 50 62 73 57
## [75,] 57 35 59 47 47 47 46 37 58 48
## [76,] 43 38 58 48 39 53 55 64 35 44
## [77,] 36 50 55 45 62 50 53 44 52 52
## [78,] 43 52 56 54 49 49 50 41 50 42
## [79,] 48 50 47 54 48 59 52 56 62 53
## [80,] 56 57 53 49 57 39 40 57 47 37
## [81,] 51 46 68 57 50 47 64 61 44 44
## [82,] 66 56 46 53 55 49 57 45 56 49
## [83,] 39 62 59 56 55 51 43 48 42 47
## [84,] 49 53 71 52 59 46 58 45 43 45
## [85,] 53 54 45 50 56 47 45 56 48 53
## [86,] 52 42 37 46 47 51 51 52 41 57
## [87,] 55 57 49 53 53 48 48 46 55 62
## [88,] 52 47 56 54 41 45 52 54 50 44
## [89,] 60 51 52 50 54 55 52 44 62 55
## [90,] 60 55 55 47 55 45 50 51 53 54
## [91,] 42 42 54 58 45 41 45 50 54 57
## [92,] 39 40 51 57 53 42 44 39 52 56
## [93,] 38 49 49 47 53 70 46 45 53 33
## [94,] 48 50 54 37 41 51 44 58 56 48
## [95,] 46 57 52 49 52 41 44 52 43 42
## [96,] 50 59 46 59 38 49 47 46 52 45
## [97,] 48 53 64 50 53 47 51 56 38 53
## [98,] 47 45 56 52 55 55 41 52 39 50
## [99,] 64 61 45 54 41 46 41 53 63 62
## [100,] 45 54 55 44 53 58 57 46 53 47Binomial
matriz_binomial <- matrix(rbinom(cantidad_elementos, size=80, prob = 0.6 ), N, n)
print(matriz_binomial)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 48 51 41 50 47 45 45 53 50 48
## [2,] 47 47 45 48 45 45 50 42 49 53
## [3,] 48 51 49 50 50 48 45 51 50 51
## [4,] 39 47 44 47 50 50 53 47 49 53
## [5,] 41 39 48 44 53 43 45 51 58 41
## [6,] 45 54 48 47 50 50 50 46 42 49
## [7,] 48 48 51 50 51 51 48 41 45 41
## [8,] 47 50 51 45 45 44 46 51 46 50
## [9,] 52 57 43 52 43 54 36 57 46 53
## [10,] 42 38 50 45 46 49 53 48 46 44
## [11,] 48 52 43 50 56 51 45 40 48 46
## [12,] 46 38 53 53 48 46 43 48 53 51
## [13,] 49 43 44 41 42 45 46 52 51 50
## [14,] 42 47 52 47 50 49 39 51 53 52
## [15,] 39 49 54 47 46 44 48 51 45 48
## [16,] 53 52 51 44 45 50 49 45 49 49
## [17,] 49 54 54 42 42 48 49 55 48 52
## [18,] 43 47 51 46 42 51 56 55 46 47
## [19,] 49 49 56 49 46 49 51 48 49 54
## [20,] 39 42 50 44 55 50 49 51 47 50
## [21,] 45 49 51 50 48 45 45 42 48 48
## [22,] 53 56 45 44 45 51 53 46 51 40
## [23,] 47 42 50 47 48 48 48 49 49 51
## [24,] 49 50 55 51 44 58 49 42 55 57
## [25,] 50 47 46 46 51 56 49 43 45 47
## [26,] 55 47 47 54 50 53 47 50 53 53
## [27,] 45 52 56 52 42 59 51 45 45 47
## [28,] 53 49 48 42 49 52 51 53 42 45
## [29,] 52 52 47 48 45 50 46 53 45 42
## [30,] 50 41 48 49 43 49 48 46 49 52
## [31,] 52 44 46 51 45 44 56 55 50 51
## [32,] 51 51 47 45 46 45 50 46 47 52
## [33,] 49 44 48 52 46 43 52 60 44 44
## [34,] 35 54 50 51 45 51 45 47 48 54
## [35,] 50 44 49 49 43 51 50 51 48 46
## [36,] 45 45 54 45 54 45 42 49 49 45
## [37,] 44 46 39 44 41 48 47 49 50 50
## [38,] 47 47 33 49 50 52 40 38 54 43
## [39,] 49 52 51 47 41 49 52 41 56 50
## [40,] 47 52 33 45 46 47 43 49 54 49
## [41,] 53 54 46 43 45 50 42 52 47 46
## [42,] 44 48 42 51 57 50 45 52 46 55
## [43,] 59 51 45 44 51 46 48 51 51 43
## [44,] 45 54 52 48 48 50 55 48 46 49
## [45,] 42 43 55 47 45 38 51 49 51 50
## [46,] 48 45 47 45 54 41 53 53 49 47
## [47,] 44 48 47 57 49 43 45 46 48 47
## [48,] 47 49 40 44 50 46 48 43 51 51
## [49,] 44 41 50 43 43 45 43 41 44 42
## [50,] 46 51 56 44 42 46 48 50 46 52
## [51,] 53 43 47 49 53 50 51 48 43 53
## [52,] 52 47 52 45 51 47 47 41 45 48
## [53,] 50 50 46 38 52 57 46 55 43 55
## [54,] 44 51 50 44 48 52 46 46 48 43
## [55,] 47 52 47 49 37 47 49 51 48 55
## [56,] 51 41 52 47 50 52 55 55 49 57
## [57,] 45 41 49 46 51 52 46 46 51 52
## [58,] 48 52 51 47 51 43 41 49 48 40
## [59,] 50 45 44 50 50 50 49 51 44 46
## [60,] 49 48 47 48 43 52 49 56 43 45
## [61,] 48 45 50 55 48 49 47 46 46 47
## [62,] 51 48 53 44 44 44 47 51 57 45
## [63,] 54 50 44 47 51 50 51 48 57 43
## [64,] 51 57 44 55 52 48 43 40 49 41
## [65,] 52 52 45 50 51 57 43 47 50 50
## [66,] 43 46 51 48 53 40 46 45 45 44
## [67,] 50 49 44 48 45 45 59 58 44 46
## [68,] 54 50 50 54 43 48 46 49 44 48
## [69,] 42 51 49 51 40 46 53 44 45 48
## [70,] 52 53 52 49 53 51 46 47 56 42
## [71,] 53 45 42 43 44 52 42 51 46 46
## [72,] 55 47 51 46 42 53 48 53 44 51
## [73,] 47 52 43 46 52 56 50 50 58 41
## [74,] 47 46 37 56 44 55 42 45 51 41
## [75,] 50 51 43 47 50 53 42 58 53 49
## [76,] 37 52 48 51 48 46 43 49 42 45
## [77,] 58 48 51 52 49 47 48 39 41 48
## [78,] 47 45 51 42 54 52 46 50 48 51
## [79,] 42 52 38 45 51 50 41 51 48 50
## [80,] 52 61 50 47 54 51 47 51 46 55
## [81,] 45 39 52 47 49 51 44 46 55 51
## [82,] 46 40 41 44 49 47 41 52 45 48
## [83,] 56 53 49 49 48 58 45 50 51 46
## [84,] 46 50 52 48 47 49 48 47 44 48
## [85,] 49 52 46 44 44 48 50 60 55 48
## [86,] 46 49 49 46 41 47 47 53 47 40
## [87,] 51 43 45 50 46 48 48 44 50 53
## [88,] 49 46 58 43 43 46 42 50 46 53
## [89,] 56 43 45 52 49 48 49 54 51 51
## [90,] 49 49 43 47 42 52 44 53 52 56
## [91,] 39 48 50 40 50 54 50 47 47 46
## [92,] 53 45 52 48 50 51 53 43 52 42
## [93,] 41 47 53 47 52 46 48 50 36 45
## [94,] 37 50 49 53 43 49 47 48 50 41
## [95,] 59 51 56 41 48 49 57 44 42 38
## [96,] 45 50 51 53 52 45 43 50 48 48
## [97,] 43 41 58 51 54 49 52 46 46 50
## [98,] 42 50 40 46 47 46 45 50 48 54
## [99,] 55 50 47 48 43 47 52 46 45 46
## [100,] 56 46 42 46 47 51 44 40 52 562. Indique claramente cual es la media y la desviacion estandar poblacional de las distribuciones mencionadas anteriormente, recuerde que existe una formula teorica para cada una de ellas
media_uniforme =mean(matriz_uniforme)
ds_uniforme =sd(matriz_uniforme)
tendencias_uniforme<- c(media_uniforme, ds_uniforme)
print(tendencias_uniforme )## [1] 50.29878 29.21024media_poisson =mean(matriz_poisson)
ds_poisson =sd(matriz_poisson)
tendencias_poisson<- c(media_poisson, ds_poisson)
media_binom =mean(matriz_binomial)
ds_binom =sd(matriz_binomial)
tendencias_binom<- c(media_binom, ds_binom)
matriz_tendencias <- rbind(tendencias_uniforme,tendencias_poisson, tendencias_binom)
nombres<-c("media", "desviacion estandar")
colnames(matriz_tendencias) <-nombres
print(matriz_tendencias) ## media desviacion estandar
## tendencias_uniforme 50.29878 29.210244
## tendencias_poisson 49.90500 7.121846
## tendencias_binom 48.05200 4.3644413. Aplique el Teorema Central del Lımite a cada muestra utilizando la media muestral respectiva en cada caso.
## SE CALCULAASN LAS MEDIAS DE CADA FILA =
media_fila_unif = rowMeans(matriz_uniforme)
media_fila_poisson = rowMeans(matriz_poisson)
media_fila_binom = rowMeans(matriz_binomial)
## normalizacion
Z_unif <- (media_fila_unif - media_uniforme) / (ds_uniforme / sqrt(n))
Z_pois <- (media_fila_poisson - media_poisson) / (ds_poisson / sqrt(n))
Z_binom <- (media_fila_binom - media_binom) / (ds_binom / sqrt(n))
valores_normalizados_df= data.frame(Z_unif, Z_pois, Z_binom)
print(valores_normalizados_df)## Z_unif Z_pois Z_binom
## 1 -0.6638621352 -0.268635110 -0.18258787
## 2 -0.2167111762 1.640672285 -0.68977640
## 3 -1.2949253138 -0.712660086 0.90424469
## 4 0.1337979407 2.928344714 -0.11013237
## 5 0.2608866861 -0.979075071 -1.26942043
## 6 -2.2891662835 1.551867290 0.03477864
## 7 -0.6113002788 0.219792363 -0.47240989
## 8 1.0803453612 0.441804851 -0.39995438
## 9 -0.9136439763 -1.778320027 0.90424469
## 10 -0.3094437360 0.575012343 -1.41433144
## 11 0.9356505448 -1.822722525 -0.11013237
## 12 0.2478579996 2.262307251 -0.11013237
## 13 1.2967644746 -0.490647598 -1.26942043
## 14 -0.1440023500 -1.067880066 0.10723415
## 15 0.2214284623 0.885829826 -0.68977640
## 16 2.0213303039 1.551867290 0.46951167
## 17 -1.3101189714 1.152244812 0.90424469
## 18 0.7252695721 -0.135427618 0.25214515
## 19 0.0605751016 0.619414841 1.41143322
## 20 0.2296019698 0.175389865 -0.25504337
## 21 0.7796823188 0.175389865 -0.68977640
## 22 -1.1692758173 -1.733917530 0.25214515
## 23 1.1609562529 -1.645112535 -0.11013237
## 24 2.9815589998 0.752622334 2.13598827
## 25 -0.6899875257 -1.245490057 -0.03767686
## 26 -1.8770024834 1.729477280 2.06353276
## 27 0.8945026436 -0.446245101 0.97670020
## 28 1.3227835897 0.042182373 0.25214515
## 29 -0.4822571674 0.219792363 -0.03767686
## 30 0.5972697674 -0.357440105 -0.39995438
## 31 -0.9372049970 1.285452304 0.97670020
## 32 -0.3028116111 0.752622334 -0.03767686
## 33 0.1764324323 -0.179830115 0.10723415
## 34 -0.1193617353 0.663817339 -0.03767686
## 35 0.1878409989 -0.579452593 0.03477864
## 36 0.2072227236 1.507464792 -0.54486539
## 37 0.3070013710 -2.621967481 -1.63169796
## 38 1.6493390053 -2.666369979 -1.99397548
## 39 0.2170011650 -0.801465081 0.54196717
## 40 1.5382769663 -0.845867579 -1.12450943
## 41 0.2264001047 1.329854802 -0.18258787
## 42 0.5582817388 -1.778320027 0.68687818
## 43 0.5142029068 -0.668257588 0.61442268
## 44 0.4704283237 -1.867125023 1.04915570
## 45 -1.0644591913 -0.179830115 -0.68977640
## 46 1.3990746263 -1.023477569 0.10723415
## 47 -1.2292436326 -0.401842603 -0.47240989
## 48 1.3279271112 -0.757062583 -0.83468741
## 49 0.3195290074 2.528722236 -3.22571905
## 50 0.9756757654 0.974634822 0.03477864
## 51 0.0003718289 -0.401842603 0.68687818
## 52 0.7880860196 -1.778320027 -0.39995438
## 53 0.0051466935 0.930232324 0.83178919
## 54 -1.5769311589 1.507464792 -0.61732090
## 55 -0.8734492177 0.397402353 0.10723415
## 56 -0.1047061009 -2.044735013 2.06353276
## 57 -0.6882658697 -0.757062583 -0.11013237
## 58 -0.3487920889 -1.733917530 -0.76223190
## 59 -0.2583366536 0.530609846 -0.11013237
## 60 -0.8232284152 -1.645112535 -0.03767686
## 61 0.6322373392 0.264194860 0.03477864
## 62 0.6978242294 -1.156685062 0.25214515
## 63 1.1722119396 0.397402353 1.04915570
## 64 -0.8159416571 -1.511905042 -0.03767686
## 65 1.8540804749 0.797024831 1.19406671
## 66 -0.5748669311 -0.757062583 -1.41433144
## 67 -1.4624747333 -0.179830115 0.54196717
## 68 0.1614244395 0.264194860 0.39705616
## 69 0.0901019328 1.640672285 -0.83468741
## 70 -0.7075205044 0.264194860 1.48388873
## 71 -0.3035044157 0.308597358 -1.19696493
## 72 -0.7233426276 -0.845867579 0.68687818
## 73 0.4322192798 0.841427329 1.04915570
## 74 0.2418136177 1.907087270 -1.19696493
## 75 0.5250560770 -0.801465081 1.12161121
## 76 1.3469742177 -0.979075071 -1.41433144
## 77 -0.5869403476 -0.002220125 0.03477864
## 78 0.5224424450 -0.579452593 0.39705616
## 79 -1.3530552421 1.329854802 -0.90714291
## 80 -1.0640047763 -0.313037608 2.42581028
## 81 -0.4588348887 1.463062295 -0.11013237
## 82 -0.6387014482 1.463062295 -1.99397548
## 83 0.5048600724 0.130987368 1.77371074
## 84 -0.8686254510 0.974634822 -0.11013237
## 85 -0.9373674822 0.352999856 1.12161121
## 86 -0.4217643010 -1.023477569 -1.12450943
## 87 0.1098809109 1.196647309 -0.18258787
## 88 -1.7971563850 -0.179830115 -0.32749888
## 89 0.5075383030 1.596269787 1.26652221
## 90 -0.3968628318 1.152244812 0.46951167
## 91 0.2631318920 -0.490647598 -0.68977640
## 92 -0.0050849861 -1.156685062 0.61442268
## 93 -1.1512954660 -0.712660086 -1.12450943
## 94 -1.4129100755 -0.535050096 -0.97959842
## 95 -0.8535332564 -0.934672574 0.32460066
## 96 0.8215662552 -0.357440105 0.32460066
## 97 0.9057355468 0.619414841 0.68687818
## 98 0.6205251610 -0.313037608 -0.90714291
## 99 1.1722871465 1.374257300 -0.11013237
## 100 -1.5681363633 0.575012343 -0.037676864. Realice un histograma con estos datos normalizados
# A partir de la normalizacion se busca imprimir el histograma
distribuciones <- list(
list(Z = Z_unif, col = "lightblue", nom = paste("Unif(1,100)\nN=", N, " n=", n)),
list(Z = Z_pois, col = "lightgreen", nom = paste("Pois(50)\nN=", N, " n=", n)),
list(Z = Z_binom, col = "lightpink", nom = paste("Binom(80,0.6)\nN=", N, " n=", n))
)
## impresion
for (distribucion in distribuciones) {
hist(distribucion$Z, freq = FALSE, col = distribucion$col, main = distribucion$nom, xlab = "Valores Z", ylab = "Densidad", xlim = c(-4, 4), ylim = c(0, 0.5))
## GENERACION DE CURVA CON LA NORMAL
curve(dnorm(x, mean = 0, sd = 1), add = TRUE, col = "black", lwd = 2.5)
}
5. Dibuje una distribucion normal est´andar sobre el histograma anterior y comente acerca de su parecido y/o diferencias con la curva normal.
Se realizo en el paso anterior la figura solapada entre la normal y los histogramas, ahora se puede apreciar diferencias interesantes. 1. Para la distribucion uniforme, es la que mas se llega a parecer con respecto a la distribucion normal, ya que trata de manter esta distribucion por los lados.
La distribucion de Poisson tiene un comportamiento casi lo mas parecido a la distribucion normal.
La distribucion binomial, esta tiene una mayor concentracion del lado derecho, podemos apreciar que graficamente esta mantiene una sesgo hacia la izquierda.
mediana_unif = median(matriz_uniforme)
mediana_poisson = median(matriz_poisson)
mediana_binom = median(matriz_binomial)
medianas_matrices <- c(mediana_unif, mediana_poisson, mediana_binom )
calcular_moda <- function(x) {
tabla_frecuencias <- table(x)
posicion_maxima <- which.max(tabla_frecuencias)
moda <- names(tabla_frecuencias)[posicion_maxima]
if (is.numeric(x)) {
return(as.numeric(moda))
}
return(moda)
}
moda_unif = calcular_moda(matriz_uniforme)
moda_poisson = calcular_moda(matriz_poisson)
moda_binom = calcular_moda(matriz_binomial)
moda_matrices <- c(moda_unif, moda_poisson, moda_binom )
matriz_analisis_medianas <- cbind(matriz_tendencias, medianas_matrices, moda_matrices)
print(matriz_analisis_medianas) ## media desviacion estandar medianas_matrices
## tendencias_uniforme 50.29878 29.210244 50.52977
## tendencias_poisson 49.90500 7.121846 50.00000
## tendencias_binom 48.05200 4.364441 48.00000
## moda_matrices
## tendencias_uniforme 1.006574
## tendencias_poisson 45.000000
## tendencias_binom 50.000000Esto para asegurar el sesgo que me dan los datos, * Uniforme, esta distribucion tiene un buen comportamiento entre su media y mediana, asi que casi no podemos decir que tiene algun sesgo. * Poisson es la que mejor se comporta que casi no tiene una inclinacion entre su media y mediana. * Para la binomial, confirmo que tiene un sesgo a la izquierda porque su mediana es mayor a la media
6. Repita los pasos anteriores para N= 1000, 10000 y n =100, 1000, (en total debera de repetir 9 veces el proceso)
N_1 = 100
N_2= 1000
N_3= 10000
n_1=10
n_2=100
n_3=1000
vector_N = c(N_1, N_2, N_3)
vector_n = c(n_1, n_2, n_3)
analizar_datos_globales <- function(m_unif, m_pois, m_binom, N, n) {
v_unif <- as.vector(m_unif)
v_pois <- as.vector(m_pois)
v_binom <- as.vector(m_binom)
#matri z de estadistica
matriz_est <- rbind(
Uniforme = c(mean(v_unif), sd(v_unif), median(v_unif), calcular_moda(v_unif)),
Poisson = c(mean(v_pois), sd(v_pois), median(v_pois), calcular_moda(v_pois)),
Binomial = c(mean(v_binom), sd(v_binom), median(v_binom), calcular_moda(v_binom))
)
colnames(matriz_est) <- c("Media", "Desv.Est", "Mediana", "Moda")
cat("\n======================================================\n")
cat(" ESTADÍSTICOS GLOBALES PARA N =", N, "y n =", n, "\n")
cat("======================================================\n")
print(round(matriz_est, 4))
}
ejecutar_tcl_y_graficar <- function(m_unif, m_pois, m_binom, N, n) {
media_uniforme <- mean(m_unif); sigma_unif <- sd(m_unif)
media_poisson <- mean(m_pois); sigma_pois <- sd(m_pois)
media_binom <- mean(m_binom); sigma_binom <- sd(m_binom)
## SE CALCULAASN LAS MEDIAS DE CADA FILA =
media_fila_unif = rowMeans(m_unif)
media_fila_poisson = rowMeans(m_pois)
media_fila_binom = rowMeans(m_binom)
## normalizacion
Z_unif <- (media_fila_unif - media_uniforme) / (ds_uniforme / sqrt(n))
Z_pois <- (media_fila_poisson - media_poisson) / (ds_poisson / sqrt(n))
Z_binom <- (media_fila_binom - media_binom) / (ds_binom / sqrt(n))
valores_normalizados_df= data.frame(Z_unif, Z_pois, Z_binom)
#print(valores_normalizados_df)
# A partir de la normalizacion se busca imprimir el histograma
distribuciones <- list(
list(Z = Z_unif, col = "lightblue", nom = paste("Unif(1,100)\nN=", N, " n=", n)),
list(Z = Z_pois, col = "lightgreen", nom = paste("Pois(50)\nN=", N, " n=", n)),
list(Z = Z_binom, col = "lightpink", nom = paste("Binom(80,0.6)\nN=", N, " n=", n))
)
## impresion
for (distribucion in distribuciones) {
hist(distribucion$Z, freq = FALSE, col = distribucion$col, main = distribucion$nom, xlab = "Valores Z", ylab = "Densidad", xlim = c(-4, 4), ylim = c(0, 0.5))
## GENERACION DE CURVA CON LA NORMAL
curve(dnorm(x, mean = 0, sd = 1), add = TRUE, col = "black", lwd = 2.5)
}
}
for(i in vector_N) {
for (j in vector_n) {
total_valores <- i * j
mat_unif <- matrix(runif(total_valores, 1, 100), nrow = i, ncol = j)
mat_pois <- matrix(rpois(total_valores, lambda = 50), nrow = i, ncol = j)
mat_binom <- matrix(rbinom(total_valores, size = 80, prob = 0.6), nrow = i, ncol = j)
analizar_datos_globales(mat_unif, mat_pois, mat_binom, i, j)
ejecutar_tcl_y_graficar(mat_unif, mat_pois, mat_binom, i, j)
}
}##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 100 y n = 10
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.4908 28.7302 48.0845 1.0778
## Poisson 50.0240 6.8962 50.0000 51.0000
## Binomial 47.9020 4.4337 48.0000 49.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 100 y n = 100
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.6368 28.6691 50.8754 1.0062
## Poisson 49.9191 7.1153 50.0000 50.0000
## Binomial 48.0414 4.3604 48.0000 47.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 100 y n = 1000
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.5853 28.4950 50.6638 27.1818
## Poisson 49.9716 7.0962 50.0000 50.0000
## Binomial 48.0187 4.3797 48.0000 48.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 1000 y n = 10
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.5616 28.4634 50.2695 1.0074
## Poisson 49.9922 7.0002 50.0000 51.0000
## Binomial 48.0217 4.4040 48.0000 49.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 1000 y n = 100
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.4591 28.5591 50.5339 37.6981
## Poisson 50.0181 7.0702 50.0000 50.0000
## Binomial 47.9864 4.3835 48.0000 48.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 1000 y n = 1000
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.4840 28.5791 50.489 1.7757
## Poisson 49.9955 7.0589 50.000 49.0000
## Binomial 48.0040 4.3804 48.000 48.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 10000 y n = 10
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.6193 28.5542 50.6849 35.8748
## Poisson 50.0583 7.0729 50.0000 49.0000
## Binomial 48.0036 4.3666 48.0000 47.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 10000 y n = 100
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.5178 28.5797 50.5568 2.5687
## Poisson 50.0010 7.0756 50.0000 50.0000
## Binomial 48.0035 4.3795 48.0000 48.0000
##
## ======================================================
## ESTADÍSTICOS GLOBALES PARA N = 10000 y n = 1000
## ======================================================
## Media Desv.Est Mediana Moda
## Uniforme 50.5089 28.5818 50.5302 17.293
## Poisson 49.9983 7.0683 50.0000 50.000
## Binomial 48.0007 4.3839 48.0000 48.000
–Conclusiones • ¿Como afectan los valores de n, N y la distribucion en cada uno de los casos respecto a la convergencia del histograma a la Normal Estandar?
En el caso de n, es uno de los elementos mas importantes, ya que es el numero de muestras que puede tener una poblacion, asi esto contribuye a la simetria y que la medida mejore conforme crece.
Para N este es el valor de casos en la muestra, por eso si es una cantidad pequenia de elementos genera que hayan valores rusticos o con ruido muy evidente, a diferencia de si son datos muy grandes que genera una mejor grafica.
En el caso de las distribuciones son diferentes entre si, asi que para converger necesitan de los parametros anteriores para asemejarse y buscar una “convergencia”, conforme estos datos crezcan.
• ¿Que acelera mas el proceso, aumentar n o N?
Dada las graficas podemos apreciar que el aumento que se realiza en N que es la cantidad de datos genera que el histograma se asemeje a la normal, no obstentante n que si bien ayuda en casos donde tienen el mismo valor, no se llega a apreciar una diferencia tan marcada como el N, pero aunque no se vea esta diferencia el tener un valor grande de n garantiza que la grafica se asemeje a la normal a diferncia de N, que solo se compactara y definira casi continua por la cantidad de datos, pero no por su dispersion.
• ¿Que distribucion converge mas rapido, porque cree que lo hace? La distribucion de Poisson es la que converge mas rapido, ya que se tiene el parametro de lambda de 50, el cual es lo suficientemente grande y ya de por si se asemeja a la normal.