PARCIAL 1
Karol Asprilla
2023-02-14
1.
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(readxl)
aleatorios <- read_excel("C:/Users/kataa/Downloads/aleatorios.xlsx")
View(aleatorios)###2. Construir e interpretar un diagrama de cajas para cada una de las variables en la base de datos.
boxplot(aleatorios$X1, horizontal = TRUE, main= 'VARIABLE X1')
Se puede observar que la mediana está un poco lejos del centro y alineada algunos datos a la izquierda, de lo cual se puede aseverar que la distancia entre el cuartil 1 y la mediana e smás pequeña, es decir, hay más datos agrupados entre el cuartil 2 y el cuartil 3. Sumando a ello, podemos observar que entre [-1,1] se encuentran gran parte de los datos y aquellos que no se encuentren en dicho rango nos refleja los sesgos.
boxplot(aleatorios$X2, horizontal = TRUE, main= 'VARIABLE X2')
Al verificar detalladamente el gráfico, podemos concluir que la mediana se encuentra en la mitad, es decir, que no hay mayores datos entre cuartiles, sino la misma cantidad. No obstante, si comparamos ambos gráficos se puede observar que tienen el mismo rango con una mayor frecuencia y un sesgo bastante amplio, pues es de al menos 2 puntos en ambos lados.
3. Construir un histograma de frecuencias relativa de las variables en la base de datos.
hist(aleatorios$X1, freq= FALSE, main='HISTOGRAMA X1')
Se puede interpretar, que la variables X1, presenta datos acampanados, es decir, parte de los datos son simétricos. Por ello, se puede observar como la mayor frecuencia se presenta en un rango entre [-1,1], mientras que los datos con una menor frecuencia estan cerca del -3 y 3.
hist(aleatorios$X2, freq= FALSE, main='HISTOGRAMA X2')
Se puede observar en el gráfico que los datos son acampanados, además como en la variable X1, se encuentra una mayor frecuencia entre el rago de [-1,1] y una menor frecuencia en -3 y 3. Sin embargo, datos cercanos al 3 y -3, se pueden considerar datos que aumentan el sesgo presentado en el gráfico, pues aunque son pocos datos su resultado corre el promedio.
4. Hallar e interpretar la media y la desviación estándar de cada una de las variables en la base de datos.
Media1=mean(aleatorios$X1)
Media1## [1] -0.03906878Al conocer el resultado de la media, podemos concluir que en promedio es más probable sacar -0.03906878 al escoger un número aleatorio entre (-3,3).
desX1=sd(aleatorios$X1)
desX1## [1] 0.990455Se puede verificar que los datos no se encuentran tan dispersos, también se puede comprobar con el dato obtenido en la media, pues al saber que la media no es mayor que la desviación, se puede comprobar que no existe mucha dispersión en los datos
mean(aleatorios$X2)## [1] 0.005467024Este dato nos confirma que es más probable que en promedio al escoger un número aleatorio entre (-3,3) su resultado sea 0.005467024.
desX2=sd(aleatorios$X2)
desX2## [1] 1.03995#####Al observar el resultado de la desviación estándar, se puede concluir que su resultado en comparación con X1 es que existe una mayor dispersión. Sin embargo, entre los datos presentados únicamente en la variable X2 no existe una mayor dispersión, que genere inefectividad en el estudio presentado.
5. Hallar el primer y tercer cuartíl de cada una de las variables en la base de datos.
quant_x1=quantile(aleatorios$X1, prob =c(0.25,0.75))
quant_x1## 25% 75%
## -0.7107604 0.6251213quant_x2=quantile(aleatorios$X2, prob=c(0.25,0.75))
quant_x2## 25% 75%
## -0.7124839 0.70505936. ¿Qué rango de datos está a una desviación estándar? (Teorema Chevysheu)
Desviacion_x1=sd(aleatorios$X1)
Desviacion_x1## [1] 0.990455Min_x1=mean(aleatorios$X1)-1*Desviacion_x1
Min_x1## [1] -1.029524Max_x1=mean(aleatorios$X1)+1*Desviacion_x1
Max_x1## [1] 0.9513862Rango_x1=aleatorios$X1[between(aleatorios$X1,Min_x1,Max_x1)]
Rango_x1## [1] -0.4711523616 0.4148614607 -0.8962319953 -0.3014326921 0.5609285836
## [6] 0.6264463082 0.1453599907 -0.8048414202 -0.9064524420 0.6107916306
## [11] 0.2542003585 0.7973540050 -0.7101448318 0.0030979663 0.2102660801
## [16] 0.2344961558 -0.3676200322 -0.2305660018 -0.9384120858 0.2834678980
## [21] 0.2183276138 0.3818172445 0.0433499281 -0.1934790816 -0.7639459909
## [26] -0.2461501936 -0.3371758339 -0.1056491783 -0.9116570254 -0.0568309133
## [31] -0.4049604740 0.8166352927 0.5482593224 -0.9594123185 0.6701498023
## [36] 0.4638150131 -0.0889701823 0.1640182745 -0.0867430572 -0.3163563633
## [41] 0.3170805485 -0.2074511940 -0.9648806554 0.7308699423 -0.5940069059
## [46] 0.0068462214 0.2443357516 0.4933235687 -0.8261758921 -0.1703028829
## [51] 0.2214630968 -0.2882495664 -0.1372472980 -0.7084713616 -0.2510410013
## [56] 0.7439234651 0.5940069059 -0.3548007044 -0.1926218829 0.8298411558
## [61] -0.8095025805 -0.0448812898 0.2198169113 0.6500795280 -0.1293744845
## [66] -0.5637048162 -0.3145873961 -0.3068805654 -0.1637863534 -0.3016725714
## [71] -0.3131412996 0.3856871444 0.2302522262 -0.7800235835 0.4915955287
## [76] -0.5266042535 0.2724959813 -0.1709236130 -0.6766754268 0.5346191756
## [81] -0.3862646736 -0.6192021829 0.8317852007 0.2659908205 -0.3654110969
## [86] -0.4501430340 -0.8964616427 0.0360000740 -0.0480213203 -0.8150357189
## [91] -0.4724347491 -0.5302104000 0.2206002137 -0.4934099707 0.2970318747
## [96] -0.5243214218 0.4679918675 -0.2271110588 -0.4702133083 -0.2284457423
## [101] -0.9193331607 -0.7381845535 -0.7249877854 0.5689139471 0.8625625014
## [106] -0.6790833140 -0.8168490240 0.8374206573 -0.5462152330 0.5722449714
## [111] -0.8048414202 -0.2754336492 -0.5455945029 0.8150357189 -0.6315735845
## [116] 0.0523107246 -0.6764844329 0.6368122740 0.5134688763 -0.1517798864
## [121] 0.3606714927 0.1863918442 -0.2582328307 0.8288702702 -0.8704682841
## [126] -0.0114368959 -0.5070205589 0.1306091235 0.6353138815 0.5678350590
## [131] -0.3263448889 -0.6640334504 -0.8363349480 0.6246796147 -0.8654501471
## [136] 0.0998818450 0.3505670065 0.2946353561 -0.5905428679 0.2273463906
## [141] -0.0707052550 -0.7548624126 0.2825925094 0.4321827873 -0.1454372978
## [146] 0.1838236585 0.4364699180 0.7549647307 0.4583694135 0.6338177627
## [151] 0.0673310296 0.0535362688 -0.1168882591 -0.8086544767 0.0469492534
## [156] 0.5502158729 -0.5610172593 -0.7216090125 0.1902071745 0.6439495337
## [161] 0.5073684406 0.1912974312 -0.6528216545 0.1604530553 0.5325023267
## [166] 0.9326049621 0.6914660844 -0.4999003522 0.6368122740 0.7585299500
## [171] 0.4708965662 0.7938911040 0.9498785403 -0.2381932518 0.2969522939
## [176] 0.7711355465 -0.7667154023 0.5689139471 -0.1784576398 0.1328476174
## [181] 0.6809136721 -0.6451728041 -0.6337234026 -0.2866545401 -0.7373819244
## [186] 0.1286798579 0.6527284313 0.5793776836 -0.5781112122 -0.8892811820
## [191] -0.6889422366 0.2213846528 0.5014612725 -0.3614889010 -0.2829108325
## [196] -0.4872845238 -0.7275775715 -0.2500939900 -0.9868017514 0.8941765373
## [201] -0.5802826308 -0.5287142812 0.4638150131 0.7066046237 0.4574349077
## [206] -0.3378238489 -1.0239546100 -0.4948788046 0.8827123565 0.2602098448
## [211] 0.1045725639 0.4767161954 0.7283756531 -0.1789237558 0.3166780971
## [216] -0.8786537364 0.7614903552 0.0972681846 0.6421623766 -0.1377884473
## [221] -0.6418804332 -0.7127050594 0.8542679097 0.5102424439 -0.0997283678
## [226] 0.6497953109 -0.0843624548 -0.3215882316 -0.4780019935 -0.3839568308
## [231] 0.6956497600 -0.0994964466 0.4339472071 -0.3206218935 0.2331591986
## [236] 0.4038815860 0.5334709385 0.4637286111 -0.0110549081 -0.6625089100
## [241] 0.7701055438 0.1980799880 -0.4489572802 -0.3281206773 0.0040154191
## [246] 0.0150328106 -0.7246899258 -0.5112008239 0.5221284027 -0.4857338354
## [251] -0.7461449059 -0.6242134987 -0.9625682651 0.4411867849 -0.6269124242
## [256] -0.3981608643 -0.8656729733 -0.3430113793 -0.8947472452 0.4141111276
## [261] -0.0743864348 -0.0766112862 0.7569997251 0.4520052244 0.4155288025
## [266] 0.8731512935 -0.1010346296 0.3213472155 0.8662300388 0.3411469152
## [271] -0.1054183940 -0.6682353160 0.0622719654 0.5153015081 0.7152721082
## [276] -0.7747462405 0.5088486432 -0.3653292424 0.0376849130 0.7956737136
## [281] -0.5899960343 -0.0174043180 0.7358767107 -0.7126072887 0.8431925380
## [286] 0.1832790986 -0.7554740478 0.1311491360 -0.4462515335 -0.5538686310
## [291] -0.4514970442 0.9393625078 0.0224542873 -0.4017238098 0.0294176061
## [296] -0.0239845122 -0.3035142981 -0.6649884199 -0.1590581178 -0.0817533419
## [301] 0.1069565769 -0.2348110684 0.7483686204 0.8744973456 0.8235974747
## [306] -0.6287746146 -0.9213204066 -0.5201127351 -0.2919193776 -0.3143463800
## [311] -0.6823620424 0.4940147846 0.3495097189 0.5726951713 0.7427127002
## [316] -0.2271110588 0.3819809535 0.3187710718 0.0304885361 -0.4922867447
## [321] 0.6461164048 -0.7597543572 -0.5782931112 0.0967293090 -0.2398462584
## [326] -0.6649884199 0.2928777576 0.8996676115 0.2639308150 -0.7634344001
## [331] 0.3821469363 -0.3248931080 0.7789867595 0.5929132385 0.0965758318
## [336] -0.8657843864 0.7108337741 0.5601214070 -0.4405967502 -0.3837931217
## [341] 0.5254628377 0.1560374585 0.2738454441 0.1722423804 0.4422827260
## [346] 0.6821687748 -0.7233973065 -1.0041276255 -0.4314267699 -0.2733690962
## [351] -0.8757319847 -0.7158655535 0.4208720839 -0.2989520453 -0.3805826054
## [356] -0.4512435225 0.0702448233 0.2356750883 0.5633467026 -0.0174804882
## [361] 0.4077014637 0.2771821528 -0.2829904133 0.3884088073 -0.3439856755
## [366] -0.7879293662 -0.3703223683 -0.6443258371 -0.7980906958 -0.1353942025
## [371] -0.4466744485 -0.5034576134 -0.5705328476 -0.8258530215 -0.2317449344
## [376] -0.8938354767 -0.5632568900 -0.4768025974 -0.8605661606 -0.5340007192
## [381] 0.5756714927 0.1781472747 0.0360000740 0.3501600077 0.4938419806
## [386] 0.0413592716 -0.7860512596 -0.8888264347 -0.0560646640 -0.1077262368
## [391] -0.7042501693 -0.7354742593 0.2429965207 0.2838669388 0.3690934136
## [396] 0.7377821021 0.3697493867 0.3174829999 -0.1865464583 0.4404284937
## [401] -0.3039144758 0.2044032499 -0.3422815098 0.7459425433 -0.0178636128
## [406] 0.9413861335 0.7160633686 -0.9725840755 0.9059908734 0.5760330168
## [411] -0.6277502962 0.3244099389 -0.1162720764 0.5057154340 -0.5749507181
## [416] -0.0731597538 -0.9597738426 0.8551501196 0.1629337021 -0.1408773187
## [421] -0.5462152330 -0.5664878699 0.6696723176 -0.6205937098 -0.4562457434
## [426] -0.1384057668 -0.3342620403 -0.3015929906 -0.9882955965 0.5324136509
## [431] -0.1927787707 -0.3085654043 -0.1065723154 -0.1832790986 -0.9337873053
## [436] -0.2455180947 0.2390584086 -0.1693706508 0.3720435870 -0.7526273293
## [441] -0.1935575256 -0.2345745997 -0.2977526492 0.0608156370 0.2685283107
## [446] 0.6048105661 -0.9040331861 -0.1158093710 0.2890465112 -0.6147604381
## [451] 0.3282013950 0.0582099347 -0.4059575076 -0.7569997251 -0.9707446225
## [456] 0.6575623956 -0.0793738764 -0.7809569524 -0.1201999567 -0.2148817657
## [461] -0.1996409082 0.7255857781 0.0003444711 0.8437382348 -0.9636619325
## [466] 0.0717784587 0.2240506092 -0.0371483111 -0.8560323295 -0.8015672393
## [471] 0.7364769772 0.1932460236 -0.9262430467 0.2319802661 0.5184506335
## [476] -0.9588052308 -0.1193529897 0.1878709099 -0.7207165709 -0.7552694115
## [481] -0.6908828709 -0.7154699233 0.1578962383 0.3651666702 -0.7892867870
## [486] 0.6329764801 0.7098492460 -0.9760287867 -0.2991919246 -0.2109698016
## [491] -0.8155689102 0.0198519956 0.7769153854 -0.1033413355 -0.3051172826
## [496] 0.5370907274 0.8393772077 -0.9841892279 -0.6118989404 -0.7252867817
## [501] -0.1810235517 -0.5776598755 0.4061234904 0.4359651484 -0.8024107956
## [506] -0.0608918072 0.0213822204 0.4557364264 0.7773292054 -0.4141111276
## [511] 0.4955711574 -0.0780687515 0.5939159564 0.5362960565 0.0327850103
## [516] -0.3533341442 0.0687111879 -0.5457718544 0.0508543962 -0.3007119176
## [521] 0.8268216334 0.2318233783 0.1076500666 0.3698312412 -0.2674175903
## [526] -0.1442776920 -0.4800608622 -0.8401389096 -0.1704574970 0.5616448107
## [531] -0.6455502444 0.2751164629 0.4211233318 0.4949652066 0.1944931682
## [536] 0.8780898497 -0.1365515345 0.0720854132 0.9296536518 -0.0784530130
## [541] -0.5837262052 0.2857780146 0.0756904228 -0.3848640517 -0.4917683327
## [546] 0.3514617219 -0.2701142421 -0.2800447874 0.0455702320 -0.5373567546
## [551] -0.7942048796 -0.4519210961 0.1456692189 -0.5734159458 0.1672765393
## [556] 0.5890865395 -0.4537014320 0.9253039934 -0.7523226486 0.6762911653
## [561] 0.3044760888 0.3733555332 0.3307059160 -0.1705348041 0.8414463082
## [566] 0.4062064818 -0.6883601600 0.7781579825 -0.5236188372 -0.5231800060
## [571] 0.3745867616 -0.1811008588 0.7548624126 0.3995683073 -0.2415004019
## [576] 0.2743217919 -0.1490718660 0.1186595000 -0.1866249022 0.1000353222
## [581] -0.4774869922 -0.3269906301 0.8168490240 -0.2635351848 0.4555670330
## [586] 0.4505659490 -0.4056244052 0.3978288987 -0.6151299203 -0.0113595888
## [591] 0.6855520951 -0.0294176061 -0.6042591849 0.2224032869 0.2124556886
## [596] 0.7659969015 -0.5750405307 -0.8341658031 -0.5997662811 0.5494155175
## [601] -0.9467612472 0.5668471204 0.0050874860 0.8978349797 0.1298371899
## [606] -0.4227115369 -0.5338245046 -0.1462876753 -0.4716662261 -0.9760287867
## [611] 0.5867218533 -0.3832155926 0.6567086075 -0.5775700629 -0.9095720088
## [616] -0.5389483704 -0.3680293048 -0.2768638296 0.4571802492 0.2414208211
## [621] -1.0036205822 -0.7867811291 -0.6784080142 -0.0593593086 -0.0142676981
## [626] 0.0028683189 -0.6251434570 -0.3611626198 -0.6772529559 -0.0544559953
## [631] -0.1112664449 -0.5080642040 0.7801270385 0.3595300768 0.3546369953
## [636] 0.1104967851 -0.5656795565 -0.3374998414 -0.2898445928 -0.4582841484
## [641] -0.3550439942 0.1926218829 -0.5264291758 -0.4315108981 -0.1798571247
## [646] -0.6577533895 -0.3974150786 -1.0270605344 0.1018042894 0.1165790309
## [651] -0.1103433078 -0.2029196366 -0.1865464583 0.3238449153 0.4313437785
## [656] -0.5006802439 -0.9582004168 0.2253841558 -0.1814123607 -0.8909864846
## [661] -0.3400919013 0.9491577657 0.2616343409 0.7719609130 -0.3979948815
## [666] 0.6203140401 0.6730260793 0.1886496648 -0.8120537132 -0.3817353900
## [671] -0.8881465874 -0.8820347830 -0.4441403689 0.0882789664 0.8723691280
## [676] 0.0796808308 -0.2451247383 -0.1078808509 0.7649714462 -0.4294963674
## [681] -0.4202036052 -0.2504884833 -0.2407909960min(Rango_x1)## [1] -1.027061max(Rango_x1)## [1] 0.9498785Desviacion_x2=sd(aleatorios$X2)
Desviacion_x2## [1] 1.03995Min_x2=mean(aleatorios$X2)-1*Desviacion_x2
Min_x2## [1] -1.034483Max_x2=mean(aleatorios$X2)+1*Desviacion_x2
Max_x2## [1] 1.045418Rango_x2=aleatorios$X2[between(aleatorios$X2,Min_x2,Max_x2)]
Rango_x2## [1] -0.368684141 -0.443042154 -0.583272595 -0.128989086 -0.212378382
## [6] 0.861230092 -0.179235258 0.384781060 0.305277581 0.261871946
## [11] 0.208467554 0.349509719 -0.427568239 0.335719506 0.569903023
## [16] 0.755371730 0.329573595 0.364921107 0.789286787 -0.444983925
## [21] -0.283946520 0.400480076 -0.223109282 0.853276561 -0.766510766
## [26] 0.077761797 0.328766419 -0.959169029 -0.120739969 -0.803888724
## [31] -0.049323035 0.945085503 0.713987447 -0.284424004 -0.317080548
## [36] -0.808017830 -0.673410341 -0.977261152 0.625888106 0.548259322
## [41] 0.321588232 0.575311105 -0.689329909 -0.737682058 -0.349834863
## [46] -0.621985237 -0.053075837 -0.120123786 -0.153482915 -0.161305707
## [51] 0.500160695 0.032019898 -0.814395662 0.566935796 -0.762513537
## [56] -0.268448730 0.241893758 -0.722006916 0.388242825 -0.868012648
## [61] -0.675426008 0.549237029 0.536208518 -0.621521394 1.043929387
## [66] -0.176125923 0.216448370 -0.825530151 -0.157896238 -0.795882897
## [71] -0.477401727 -0.155650923 -0.352195002 0.426562110 -0.513643954
## [76] 0.698184976 -0.638968913 0.726281542 1.008188519 -0.480060862
## [81] 0.704642389 0.045110937 0.780437404 -0.056140834 -0.099958015
## [86] -0.723000539 -0.531356363 0.391792128 0.368029305 -0.898521648
## [91] -0.563168214 -0.246307081 0.025208919 -0.470383839 -0.787094905
## [96] -0.818131412 -1.013672772 0.704544618 0.075921207 -0.148144181
## [101] 0.148066874 0.416029025 -0.813649876 -0.049246864 -0.444647412
## [106] 0.318448201 -0.499986754 -0.558065949 -0.435376251 1.017388058
## [111] 0.576123966 -0.574589194 -0.851186996 -0.148453410 0.539744178
## [116] -0.411695282 0.646775788 0.072161583 -0.575221293 0.103341335
## [121] -0.459899638 -0.146751518 -0.671875569 -0.350567007 -0.199172518
## [126] 0.315874331 0.557349722 -1.023438472 0.618831564 0.635689048
## [131] -0.793575055 0.718537194 0.485820237 0.017098500 -0.614113560
## [136] 0.044344688 -1.017131126 0.843410817 0.303193701 0.215821956
## [141] 0.965001163 0.128834472 -0.503891897 -0.585723683 0.618831564
## [146] 0.602699401 0.002944489 -0.928712325 -0.518361958 -0.765689947
## [151] 0.303193701 0.185068529 -0.605546120 -0.506672677 0.197455847
## [156] -0.942577572 0.126520945 -0.784802978 -0.701311365 0.658133104
## [161] 0.473290811 -0.365574806 0.268289568 0.056523959 0.428574367
## [166] 0.083979330 0.481693405 -0.651687060 -0.561553861 -0.943891791
## [171] -0.235675088 -0.989666660 -0.207998028 0.884067504 -0.465604444
## [176] 0.175270998 -0.816103238 0.286017894 0.624120275 0.315793613
## [181] -0.811946848 -0.037225618 0.525726591 0.727079623 -0.398657676
## [186] -0.482896212 -0.823597475 -0.341470923 0.677349590 -0.682941845
## [191] -0.559944056 -0.310732275 0.059512786 0.441777956 -0.247332537
## [196] 0.297911811 0.745437774 0.757611360 0.901618478 0.541249392
## [201] -0.018092123 -0.764664492 -0.222325980 -0.816529564 -0.634472599
## [206] -0.306399670 1.023568075 1.036178219 0.019622348 -0.760367129
## [211] 0.976890533 0.457519036 -0.710340373 -0.004934009 0.036153551
## [216] 0.222952394 -0.270114242 -0.504326181 0.664797426 -0.007687504
## [221] -0.146210368 0.415778914 -0.011666543 -0.390471087 0.245913725
## [226] -0.051085181 0.339282451 0.562988589 -0.001950866 0.596289738
## [231] 0.933787305 0.661461854 -0.075538082 -0.453785560 -0.054685643
## [236] 0.490991852 -0.841555448 -0.377788183 -0.630174100 0.901848125
## [241] 0.246543550 0.481863935 0.080524387 -0.694188884 -0.945324246
## [246] 0.514428393 -0.648474270 0.546481260 0.438069492 0.198861017
## [251] -0.250962557 0.544617933 -0.824670678 0.288887350 0.828438260
## [256] -0.624957011 0.345528406 0.241972202 -0.672066562 0.456840326
## [261] 0.331593810 0.110266001 -0.283308736 -0.927066139 -0.050472408
## [266] 0.640940243 0.062577783 -0.861452918 0.468846793 -0.249067398
## [271] -0.692048161 0.612820941 0.919217200 -0.518537036 -0.221698429
## [276] 0.330301191 -0.259814215 0.824240942 0.801251190 -1.025766778
## [281] 0.599583245 -1.024729954 -0.559853106 0.502675448 0.562540663
## [286] -0.266784355 0.595284746 0.249619916 -0.317966169 -0.965246727
## [291] -0.580282631 0.464495997 -0.500160695 -0.259576609 0.247648586
## [296] -0.702389116 -0.339282451 0.031407126 0.363449999 -0.155263251
## [301] -0.904492481 -0.297911811 0.165182428 0.006310756 -0.139641543
## [306] 0.793365871 -0.998443284 -0.118890284 0.264168420 -0.365492951
## [311] -0.139023086 -0.783657015 -0.248988954 -0.711620487 0.851407549
## [316] -0.920736056 0.834816092 0.084977501 0.043426098 0.362713308
## [321] -0.272336820 -0.174184152 0.037531436 0.815462045 -0.586539954
## [326] 0.467480277 -0.472264219 0.696234110 -0.439416681 0.478001994
## [331] 0.157276645 -0.353904852 0.635594688 0.431595026 0.115423973
## [336] 1.034738943 -0.271304543 -0.940076461 -0.314828412 0.681588972
## [341] 0.828006250 -0.582366511 -0.181489668 -0.088894012 -0.282910833
## [346] -0.834384082 -0.535501385 0.878765150 0.853606252 -0.498166628
## [351] -0.252462087 -0.805264335 -0.508413223 -0.828438260 -0.934614945
## [356] 0.212925215 -0.357163117 0.419952357 0.518712113 -0.080141263
## [361] 0.626073415 -0.108265112 0.399320470 0.953007202 -0.291041715
## [366] 0.512334282 0.152940629 0.543375336 0.331109504 0.547281616
## [371] 0.722006916 -0.558333113 0.221306209 0.343742386 -0.402801561
## [376] 1.031087322 -0.754455414 0.340741053 0.483669282 -0.158670446
## [381] -0.022530457 0.087663921 -0.581821951 -0.004781668 0.494360393
## [386] -0.285698434 -0.650929906 -0.435628635 -0.013578756 -0.611621545
## [391] -0.014726993 0.458284148 -0.352113148 -0.960503712 0.421623554
## [396] 0.167508460 -0.071241857 -0.670725058 0.750800382 -0.717843704
## [401] -0.853497113 -0.004704361 0.209952304 0.484701559 0.117427135
## [406] 0.682362042 -0.845047907 0.475773732 -0.699162683 -0.542223688
## [411] -0.001339231 -0.653579946 -0.313382316 0.014649686 0.803045168
## [416] 0.889053808 0.193635969 0.873824320 -0.727777660 0.510939344
## [421] 0.751308562 0.592913239 -0.280761014 -0.567924872 -0.649417871
## [426] -0.600407475 0.894633558 0.257520014 0.933905540 0.447266757
## [431] 0.818345143 -0.180011739 0.921086212 0.252462087 0.006846221
## [436] 0.926243047 0.837312655 0.544883960 -0.176747790 0.522040864
## [441] -0.020464768 -0.414861461 0.065260792 0.771856321 -0.550394361
## [446] -0.632882120 -0.763741355 -0.379843641 -0.538240101 -0.945565262
## [451] 0.649985168 -0.715074293 -0.099266799 -0.280442691 -0.801460374
## [456] -0.437817107 -0.621613481 -0.701703584 0.196052952 -0.830921181
## [461] 0.553154678 0.195661869 0.490647381 -0.367701887 0.731070031
## [466] -0.137015377 0.788763828 0.362224455 0.177758466 -0.735976755
## [471] -0.005852598 0.109957909 0.810778147 0.314828412 0.202606998
## [476] 0.149614152 -0.604443358 0.217858087 -0.691077275 -0.643667590
## [481] -0.629333954 -0.037455266 0.320300160 -0.095346877 0.385522299
## [486] -0.161537628 -0.283388317 0.994423317 0.271543286 0.515301508
## [491] 0.086051841 0.894176537 0.001950866 0.253805865 0.589177489
## [496] -0.097345492 -0.792003902 0.016868853 -0.048787570 0.269637894
## [501] -0.405541414 0.981833637 0.960988018 -0.358795660 -0.064341066
## [506] 0.338147856 0.741403028 0.109650955 -0.190441369 -0.611253199
## [511] 0.339848611 -0.259022954 0.607384436 -0.719725222 0.093963308
## [516] 0.458539944 -0.796408131 0.511723783 0.834384082 0.544617933
## [521] 0.175039077 0.315633315 -0.275433649 1.018670446 0.288009687
## [526] -0.616424813 -0.202919637 0.564691618 0.770414772 -0.668331950
## [531] 0.424302016 0.526165422 0.488577143 0.866230039 0.462962362
## [536] 0.205653805 0.873599220 -0.717545845 -0.682264272 0.051927600
## [541] -0.379595804 -0.780230494 -0.177446964 0.087511580 -0.783138603
## [546] 0.351706149 -0.590451918 0.667375843 -0.101034630 0.916652425
## [551] -0.430839009 0.177835773 0.113421947 0.062807430 -0.700529199
## [556] 0.362877017 0.814823125 -0.593643108 0.276149876 0.112497673
## [561] -0.571344572 -0.360590775 -0.095423047 0.609961717 -0.894176537
## [566] -0.050854396 -0.678601282 0.748875664 0.739491952 0.099189492
## [571] 0.107726237 0.309207735 0.667375843 0.144277692 0.706310175
## [576] 0.524496500 0.245754563 -0.337823849 -0.054302518 -0.237799895
## [581] -0.210734470 -0.327797807 -0.582638222 0.850308197 0.527484190
## [586] 0.642162377 -0.988545708 -0.498773716 0.630548129 -1.030307430
## [591] 0.929771886 -0.022760105 -0.920967977 0.325619567 0.146442289
## [596] 0.393114306 0.828331395 0.739792085 -0.029724561 -0.662128059
## [601] 0.143813850 -0.775364697 -0.679854111 -0.698967142 0.012125838
## [606] -0.352845291 -0.449549589 -0.110496785 0.075231128 -0.081753342
## [611] 0.516874934 -0.320621893 0.107341975 0.169991381 0.186001898
## [616] -0.957472821 0.609777544 -0.908762559 0.506238393 0.246623131
## [621] 0.441862085 -0.795778305 -0.720121989 -0.476973128 0.264089977
## [626] 0.128063675 0.960624220 0.372125442 -0.940908649 0.686422936
## [631] -0.879665549 0.360264494 0.346665274 -0.381241989 0.534265610
## [636] 0.009371206 0.047562025 -0.474317403 -0.857910436 -1.030828116
## [641] 0.856143743 -0.138714995 0.086896534 -0.114577006 0.490560979
## [646] 0.075997377 0.157585873 0.259497028 -0.561017259 0.099881845
## [651] -0.101957767 -0.419869366 0.196598648 0.130609124 -0.258311275
## [656] -0.151702579 -0.766715402 -0.325619567 0.748570983 0.727179668min(Rango_x2)## [1] -1.030828max(Rango_x2)## [1] 1.0439297. Con la información obtenida indique si los datos presentan sesgo o no.
Al separar aquellos datos que se encuentran alejados de los mínimos y máximos, gran parte de los datos sesgados o datos atípicos de la muestra se omiten, pues al ser datos tan sesgados, afectan la efectividad del estudio. Por ello, si se hace una comparación con los datos iniciales para ambas variables que son 1000 y luego de observan los datos que se encuentran fuera de los rangos del máximo y mínimo podemos afirmar que en la variables X1 se suprimieron alrededor de 317 datos, mientras que para la variables X2 se fueron 340. Por lo cual, se puede afirmar que existia al menos un 31.7% de los datos en la variable X1 y un 34% en la variables X2 se encontraban sesgados. Sin embargo, al verificar la desviación estándar, se demuestra que el sesgo no es excesivo y que por el contrario existe un menor sesgo del que se esperaba al ser datos aleatorios.
8. Utilice la regla empírica para dar el rango de datos que contiene a casi el 98 % de los valores de los datos
Min_1=mean(aleatorios$X1)-2*Desviacion_x1
Min_1## [1] -2.019979Max_1=mean(aleatorios$X1)+2*Desviacion_x1
Max_1## [1] 1.941841Rango_1=aleatorios$X1[between(aleatorios$X1,Min_1,Max_1)]
Rango_1## [1] -0.4711523616 0.4148614607 -0.8962319953 -0.3014326921 0.5609285836
## [6] -1.7219099391 0.6264463082 0.1453599907 -0.8048414202 -0.9064524420
## [11] 0.6107916306 -1.5240084394 0.2542003585 0.7973540050 -0.7101448318
## [16] 0.0030979663 -1.2848113329 0.2102660801 0.2344961558 -0.3676200322
## [21] -0.2305660018 -1.4544639271 -0.9384120858 0.2834678980 0.2183276138
## [26] 0.3818172445 0.0433499281 -0.1934790816 -0.7639459909 1.0394546734
## [31] -1.3563339962 -0.2461501936 -0.3371758339 -0.1056491783 -0.9116570254
## [36] -0.0568309133 -0.4049604740 0.8166352927 0.5482593224 1.3557564671
## [41] -0.9594123185 0.6701498023 1.7966567611 0.4638150131 -0.0889701823
## [46] 0.9912923815 -1.3849057723 0.1640182745 -0.0867430572 -0.3163563633
## [51] 0.3170805485 -0.2074511940 -0.9648806554 0.7308699423 -0.5940069059
## [56] 0.0068462214 0.2443357516 1.6146441340 0.4933235687 -0.8261758921
## [61] 1.4080251276 -0.1703028829 0.2214630968 -0.2882495664 -0.1372472980
## [66] -1.4274610294 -0.7084713616 -1.1366523722 0.9528866940 -0.2510410013
## [71] -1.9107847038 0.7439234651 1.0702797226 0.5940069059 -1.0619078239
## [76] 1.3646331354 1.0013445717 -0.3548007044 -0.1926218829 0.8298411558
## [81] -0.8095025805 -0.0448812898 0.2198169113 0.6500795280 -0.1293744845
## [86] -0.5637048162 -0.3145873961 -1.1398697097 -0.3068805654 -0.1637863534
## [91] 1.0198300515 -0.3016725714 -0.3131412996 1.1472229744 0.3856871444
## [96] 0.2302522262 -0.7800235835 0.4915955287 -0.5266042535 -1.4993111108
## [101] 0.2724959813 1.1537485989 -0.1709236130 -0.6766754268 0.5346191756
## [106] -1.8047830963 -0.3862646736 -0.6192021829 0.8317852007 1.4105035007
## [111] 0.2659908205 -1.6560079530 -0.3654110969 -0.4501430340 -0.8964616427
## [116] 1.0422172636 0.0360000740 -0.0480213203 -0.8150357189 -0.4724347491
## [121] -0.5302104000 0.2206002137 -1.2629425328 1.2685654838 1.1340284800
## [126] -0.4934099707 0.2970318747 -1.2282134776 -0.5243214218 0.4679918675
## [131] -0.2271110588 -0.4702133083 -0.2284457423 -0.9193331607 -0.7381845535
## [136] 1.8348328013 -0.7249877854 0.9669543033 1.4037095752 0.5689139471
## [141] 0.8625625014 -1.5109435481 -0.6790833140 -1.7242746253 -0.8168490240
## [146] -1.2939449334 0.8374206573 -0.5462152330 0.5722449714 -0.8048414202
## [151] -0.2754336492 -0.5455945029 0.8150357189 -0.6315735845 0.0523107246
## [156] -0.6764844329 -1.2129066818 0.6368122740 1.6530020730 -1.6878857423
## [161] 0.5134688763 -0.1517798864 0.3606714927 0.1863918442 1.2414966477
## [166] -0.2582328307 0.8288702702 -0.8704682841 -0.0114368959 1.1928773347
## [171] -1.6942794900 -0.5070205589 0.1306091235 0.6353138815 -1.4245006241
## [176] 1.0952999219 0.5678350590 -0.3263448889 -0.6640334504 -0.8363349480
## [181] 0.6246796147 -1.0472331269 -1.1416273082 -0.8654501471 0.0998818450
## [186] 0.3505670065 0.2946353561 1.4302213458 -0.5905428679 0.2273463906
## [191] -0.0707052550 -0.7548624126 -1.4379202185 1.0677058526 0.2825925094
## [196] 0.4321827873 1.5524756236 -0.1454372978 0.1838236585 0.4364699180
## [201] 0.7549647307 0.4583694135 -1.2827194951 0.6338177627 0.0673310296
## [206] 0.0535362688 1.0199573808 0.9539712664 -0.1168882591 -0.8086544767
## [211] 1.0186704458 0.0469492534 0.5502158729 -0.5610172593 -0.7216090125
## [216] 1.3548014977 0.1902071745 1.7551974452 0.6439495337 0.5073684406
## [221] 0.1912974312 -1.2941200112 -0.6528216545 0.1604530553 0.5325023267
## [226] 1.2306554709 0.9326049621 0.6914660844 -0.4999003522 0.6368122740
## [231] -1.5830664779 0.7585299500 0.4708965662 0.7938911040 1.6853482521
## [236] 0.9498785403 -0.2381932518 0.2969522939 1.2895407053 1.6323610907
## [241] 0.7711355465 -0.7667154023 0.5689139471 -0.1784576398 1.7066167857
## [246] 0.1328476174 -1.3154453882 0.6809136721 -1.9262006390 -0.6451728041
## [251] -0.6337234026 -0.2866545401 -0.7373819244 0.1286798579 0.6527284313
## [256] 0.5793776836 -0.5781112122 -0.8892811820 -0.6889422366 -1.3040835256
## [261] 0.9566269910 0.2213846528 0.5014612725 -1.7036700228 -1.4420220396
## [266] -0.3614889010 -0.2829108325 -0.4872845238 -0.7275775715 -1.0514781934
## [271] -1.8250375433 -1.3829117052 -0.2500939900 -0.9868017514 0.8941765373
## [276] -0.5802826308 -0.5287142812 -1.3859016690 -1.5542673282 0.4638150131
## [281] 0.7066046237 0.4574349077 -0.3378238489 1.6548028725 1.6095964384
## [286] -1.0239546100 -1.4270381143 -0.4948788046 0.8827123565 -1.4709667084
## [291] 0.2602098448 -1.0647340787 0.1045725639 0.4767161954 -1.6542026060
## [296] 0.7283756531 -0.1789237558 0.3166780971 -0.8786537364 0.7614903552
## [301] 0.0972681846 0.6421623766 1.7162119548 -0.1377884473 -0.6418804332
## [306] -1.7056299839 -1.6059721020 -0.7127050594 0.8542679097 0.5102424439
## [311] -0.0997283678 1.2820214579 0.6497953109 -0.0843624548 -1.9502294890
## [316] 1.4467968867 -0.3215882316 -0.4780019935 -0.3839568308 0.6956497600
## [321] -0.0994964466 0.4339472071 -0.3206218935 -1.7491584003 0.2331591986
## [326] 0.4038815860 0.5334709385 0.4637286111 1.2602276911 -0.0110549081
## [331] 1.1757560969 -0.6625089100 1.1148836165 1.7612956071 0.7701055438
## [336] 0.1980799880 -0.4489572802 -1.1470751815 -0.3281206773 0.0040154191
## [341] 0.0150328106 -1.0842177289 -1.5661498765 -0.7246899258 -1.2438135855
## [346] -0.5112008239 0.5221284027 -0.4857338354 -0.7461449059 -0.6242134987
## [351] -1.8028367776 1.4864872355 -0.9625682651 1.0239546100 0.4411867849
## [356] -0.6269124242 -0.3981608643 -0.8656729733 -0.3430113793 -0.8947472452
## [361] 0.4141111276 -1.7020374798 -0.0743864348 -1.3640510588 -1.1414817891
## [366] -0.0766112862 1.0112444215 0.7569997251 0.4520052244 0.4155288025
## [371] 1.2725104170 0.8731512935 -1.4608849597 1.7138791009 -0.1010346296
## [376] -1.6566082195 0.3213472155 0.8662300388 0.9994528227 0.3411469152
## [381] -0.1054183940 -0.6682353160 1.3747967387 0.0622719654 -1.2900682123
## [386] 0.5153015081 -1.5418436305 0.7152721082 -0.7747462405 -1.6575177142
## [391] 0.5088486432 -0.3653292424 0.0376849130 -1.2656619219 -1.0893290892
## [396] 0.7956737136 -0.5899960343 -0.0174043180 -1.2992632037 0.7358767107
## [401] -0.7126072887 0.8431925380 -1.8206083041 0.1832790986 -0.7554740478
## [406] 0.1311491360 -0.4462515335 -0.5538686310 -0.4514970442 1.0611006473
## [411] 0.9393625078 0.0224542873 -0.4017238098 0.0294176061 1.1285146684
## [416] -0.0239845122 -0.3035142981 -0.6649884199 -0.1590581178 -0.0817533419
## [421] 0.1069565769 -1.2413283912 -0.2348110684 -1.4633360479 0.7483686204
## [426] 1.2021223483 1.7901629690 1.1967813407 0.8744973456 0.8235974747
## [431] -1.2464715837 -1.2191549104 -0.6287746146 -0.9213204066 -0.5201127351
## [436] -0.2919193776 0.9808422874 -0.3143463800 -0.6823620424 0.4940147846
## [441] 0.3495097189 0.5726951713 0.7427127002 -0.2271110588 0.3819809535
## [446] 0.3187710718 1.0229223335 0.0304885361 -0.4922867447 1.1121801435
## [451] 0.6461164048 0.9897917153 -0.7597543572 1.3312364899 -0.5782931112
## [456] 0.0967293090 -0.2398462584 -0.6649884199 0.2928777576 -1.1746874407
## [461] 0.8996676115 1.3747967387 0.2639308150 -0.7634344001 -1.0800977179
## [466] 0.3821469363 -0.3248931080 -1.2735426935 0.7789867595 0.5929132385
## [471] -1.6818739823 -1.0679764273 0.0965758318 -0.8657843864 -1.5622526917
## [476] 0.7108337741 0.5601214070 1.3839076018 -0.4405967502 -0.3837931217
## [481] 0.5254628377 0.1560374585 -1.0418216334 0.2738454441 0.1722423804
## [486] 0.4422827260 0.6821687748 -0.7233973065 -1.0041276255 -0.4314267699
## [491] -0.2733690962 -0.8757319847 -0.7158655535 0.4208720839 1.0616395230
## [496] -0.2989520453 -0.3805826054 -0.4512435225 0.0702448233 0.2356750883
## [501] 1.2916507330 0.5633467026 -1.0640610526 -0.0174804882 -1.5601835912
## [506] -1.2078135114 0.4077014637 -1.7132151697 0.2771821528 -0.2829904133
## [511] 0.3884088073 0.9970608517 -0.3439856755 1.1472229744 -0.7879293662
## [516] -0.3703223683 -0.6443258371 -0.7980906958 -0.1353942025 -0.4466744485
## [521] 1.2347436495 -0.5034576134 -1.6076410247 -0.5705328476 -0.8258530215
## [526] -0.2317449344 -1.2646432879 -0.8938354767 -0.5632568900 -0.4768025974
## [531] 1.1475185602 -0.8605661606 -0.5340007192 0.5756714927 1.0553435459
## [536] 0.1781472747 0.0360000740 0.3501600077 1.0266717254 0.4938419806
## [541] 0.0413592716 -1.9824801711 -0.7860512596 -0.8888264347 -0.0560646640
## [546] -0.1077262368 -0.7042501693 -0.7354742593 0.2429965207 0.2838669388
## [551] 1.3603767002 0.3690934136 -1.6762351152 -1.7428374122 0.7377821021
## [556] 0.3697493867 0.3174829999 -0.1865464583 0.4404284937 -0.3039144758
## [561] 0.2044032499 -0.3422815098 0.7459425433 -1.9684830477 -0.0178636128
## [566] 0.9413861335 -1.9165145204 0.7160633686 -0.9725840755 0.9059908734
## [571] 0.5760330168 1.1851216186 -0.6277502962 0.3244099389 -0.1162720764
## [576] 0.5057154340 -0.5749507181 -0.0731597538 -0.9597738426 0.8551501196
## [581] 0.1629337021 -0.1408773187 -0.5462152330 -0.5664878699 1.3189060155
## [586] 1.2723376130 0.6696723176 -0.6205937098 1.0283588381 -1.0678422768
## [591] -0.4562457434 1.3255066733 -0.1384057668 -0.3342620403 -0.3015929906
## [596] -0.9882955965 0.5324136509 -0.1927787707 1.2317991605 -0.3085654043
## [601] -0.1065723154 -0.1832790986 -1.2811506167 -1.7225829652 1.4102988644
## [606] -1.3811222743 -1.2911232261 -0.9337873053 -0.2455180947 0.2390584086
## [611] -0.1693706508 0.3720435870 -0.7526273293 -0.1935575256 -0.2345745997
## [616] -0.2977526492 0.0608156370 0.2685283107 0.6048105661 -0.9040331861
## [621] -0.1158093710 0.2890465112 -0.6147604381 0.3282013950 0.0582099347
## [626] -0.4059575076 -1.0660846783 -1.6434796635 -0.7569997251 1.1384054233
## [631] -0.9707446225 0.6575623956 -0.0793738764 -0.7809569524 -0.1201999567
## [636] -0.2148817657 -0.1996409082 0.7255857781 0.0003444711 0.8437382348
## [641] -1.5879049897 -0.9636619325 -1.2773375602 0.0717784587 0.2240506092
## [646] -0.0371483111 -0.8560323295 -0.8015672393 0.9909172149 0.7364769772
## [651] 0.1932460236 1.7442334865 -0.9262430467 0.2319802661 1.6768626665
## [656] 0.5184506335 -0.9588052308 -0.1193529897 0.1878709099 -0.7207165709
## [661] -0.7552694115 -0.6908828709 -0.7154699233 0.1578962383 0.3651666702
## [666] -1.3742055671 -0.7892867870 1.1425095181 0.6329764801 0.7098492460
## [671] 1.4033003026 -0.9760287867 -0.2991919246 -0.2109698016 1.0496205505
## [676] -0.8155689102 0.0198519956 0.7769153854 -0.1033413355 -0.3051172826
## [681] 0.5370907274 0.8393772077 -0.9841892279 -0.6118989404 -1.0706867215
## [686] -0.7252867817 -0.1810235517 1.3650196706 1.3496469364 -0.5776598755
## [691] 1.4716442820 0.4061234904 1.2858595255 0.4359651484 -0.8024107956
## [696] -0.0608918072 0.0213822204 0.4557364264 -1.5423438526 0.7773292054
## [701] -0.4141111276 0.4955711574 -0.0780687515 -1.7341699277 0.5939159564
## [706] 1.1714928405 0.5362960565 0.0327850103 -0.3533341442 0.0687111879
## [711] -1.2355667423 -1.3139924704 -0.5457718544 0.0508543962 -0.3007119176
## [716] 0.8268216334 0.2318233783 0.1076500666 0.3698312412 -0.2674175903
## [721] -0.1442776920 -0.4800608622 -0.8401389096 -0.1704574970 -1.1430961422
## [726] 0.5616448107 -0.6455502444 0.2751164629 0.4211233318 0.4949652066
## [731] 0.1944931682 -1.8745504349 1.8763330445 -1.2907707969 0.8780898497
## [736] -0.1365515345 0.0720854132 -1.2607370081 0.9296536518 -1.3422663869
## [741] -0.0784530130 1.4837223716 -0.5837262052 0.2857780146 1.2571899788
## [746] 1.0570806808 0.0756904228 -1.1333008842 -0.3848640517 -0.4917683327
## [751] 0.3514617219 -0.2701142421 -0.2800447874 -1.0882195056 0.0455702320
## [756] -1.2566829355 -0.5373567546 1.5227897165 -0.7942048796 -0.4519210961
## [761] 1.3076714822 0.1456692189 -0.5734159458 -1.7555521481 0.1672765393
## [766] 0.5890865395 -0.4537014320 0.9253039934 -0.7523226486 0.6762911653
## [771] 0.3044760888 0.3733555332 0.3307059160 -0.1705348041 1.2811506167
## [776] 0.8414463082 0.4062064818 -0.6883601600 1.6294688976 0.7781579825
## [781] -0.5236188372 -1.2663440430 -0.5231800060 0.3745867616 1.3947510524
## [786] -0.1811008588 1.3628869056 0.7548624126 0.3995683073 1.7414367903
## [791] -1.1821930457 -0.2415004019 1.7327920432 0.2743217919 -1.4689385353
## [796] -0.1490718660 0.1186595000 -0.1866249022 0.1000353222 -1.0325220501
## [801] -1.9595336198 -1.0803705663 -0.4774869922 -0.3269906301 0.8168490240
## [806] -0.2635351848 0.4555670330 0.4505659490 -0.4056244052 0.3978288987
## [811] -0.6151299203 -0.0113595888 0.6855520951 0.9515633792 -1.4148599803
## [816] -0.0294176061 -0.6042591849 0.2224032869 -1.1695192370 1.1757560969
## [821] 0.2124556886 0.7659969015 -0.5750405307 1.7928277884 -0.8341658031
## [826] -0.5997662811 0.5494155175 -0.9467612472 0.5668471204 0.0050874860
## [831] 0.8978349797 0.1298371899 -0.4227115369 -0.5338245046 -0.1462876753
## [836] -0.4716662261 -0.9760287867 0.5867218533 -0.3832155926 0.6567086075
## [841] -0.5775700629 -1.6203057385 -1.0526764527 -0.9095720088 -0.5389483704
## [846] -1.4213446775 -0.3680293048 -0.2768638296 -1.1728593563 0.4571802492
## [851] 0.2414208211 -1.0036205822 -1.0564122022 -0.7867811291 -1.2048053577
## [856] -0.6784080142 0.9989480532 -1.4729994291 -0.0593593086 -0.0142676981
## [861] 0.0028683189 -0.6251434570 -0.3611626198 -1.2541590877 -0.6772529559
## [866] -0.0544559953 -0.1112664449 -0.5080642040 0.7801270385 0.3595300768
## [871] 0.3546369953 0.1104967851 1.7856245904 1.3869021132 1.6358535504
## [876] -0.5656795565 -0.3374998414 1.6191688701 -1.0757207747 -0.2898445928
## [881] -0.4582841484 -0.3550439942 -1.0402436601 0.1926218829 -0.5264291758
## [886] -0.4315108981 -1.6878857423 -1.4100896806 -0.1798571247 -0.6577533895
## [891] -1.1592715055 -0.3974150786 -1.0270605344 0.1018042894 -1.2782038539
## [896] 1.3915223462 0.1165790309 -0.1103433078 -0.2029196366 -0.1865464583
## [901] 0.3238449153 1.1935026123 0.4313437785 1.6194553609 -0.5006802439
## [906] 1.1518159226 1.3290127754 -0.9582004168 0.2253841558 -0.1814123607
## [911] -0.8909864846 -1.2082909961 -0.3400919013 1.1544921108 0.9491577657
## [916] 0.2616343409 1.0231792658 -1.5716523194 0.7719609130 1.4392139747
## [921] -0.3979948815 0.6203140401 0.6730260793 0.1886496648 1.7334787117
## [926] -0.8120537132 -0.3817353900 -0.8881465874 -0.8820347830 -0.4441403689
## [931] -1.6188823793 1.3661883713 1.3483168004 0.0882789664 1.8627179088
## [936] 1.6888407117 -1.2317991605 0.8723691280 0.0796808308 -1.1056727089
## [941] -0.2451247383 -0.1078808509 0.7649714462 1.4993111108 -0.4294963674
## [946] 1.3538419807 -0.4202036052 -0.2504884833 -0.2407909960 1.0769508663
## [951] 0.9674408830min(Rango_1)## [1] -1.98248max(Rango_1)## [1] 1.876333Min_2=mean(aleatorios$X2)-2*Desviacion_x2
Min_2## [1] -2.074434Max_2=mean(aleatorios$X2)+2*Desviacion_x2
Max_2## [1] 2.085368Rango_2=aleatorios$X2[between(aleatorios$X2,Min_2,Max_2)]
Rango_2## [1] -0.368684141 -1.134901595 -0.443042154 1.110338417 -0.583272595
## [6] 1.200862698 -0.128989086 1.091268587 -1.370676728 -0.212378382
## [11] 0.861230092 -0.179235258 0.384781060 -1.377952685 0.305277581
## [16] 0.261871946 0.208467554 0.349509719 -1.912685548 -0.427568239
## [21] 1.774433258 0.335719506 0.569903023 0.755371730 1.647331374
## [26] 0.329573595 0.364921107 0.789286787 -0.444983925 -0.283946520
## [31] -1.543603503 0.400480076 -0.223109282 -1.143096142 1.232779141
## [36] -1.585481186 0.853276561 -0.766510766 0.077761797 0.328766419
## [41] -0.959169029 -0.120739969 -0.803888724 -0.049323035 0.945085503
## [46] 1.065814104 0.713987447 -0.284424004 -0.317080548 -0.808017830
## [51] 1.145451733 -1.380130925 -0.673410341 -1.197408892 1.860989869
## [56] -0.977261152 1.430221346 0.625888106 0.548259322 0.321588232
## [61] 0.575311105 -1.139721917 -1.161972705 -1.938578862 -0.689329909
## [66] -0.737682058 -0.349834863 -0.621985237 -0.053075837 -0.120123786
## [71] -1.390917532 -0.153482915 1.259045348 -0.161305707 0.500160695
## [76] 0.032019898 -0.814395662 0.566935796 -0.762513537 -0.268448730
## [81] -1.658727342 0.241893758 -0.722006916 0.388242825 -0.868012648
## [86] -2.008810043 1.380526555 -0.675426008 0.549237029 0.536208518
## [91] -0.621521394 -1.790922397 1.043929387 -0.176125923 1.795888238
## [96] -1.982480171 0.216448370 -0.825530151 -1.305156729 -0.157896238
## [101] -0.795882897 -0.477401727 -0.155650923 -0.352195002 0.426562110
## [106] 1.496491677 -0.513643954 -1.674989107 -1.444404916 0.698184976
## [111] -0.638968913 0.726281542 1.718217391 1.008188519 -0.480060862
## [116] 1.465568857 0.704642389 0.045110937 1.644662007 0.780437404
## [121] -1.326980055 -0.056140834 -0.099958015 -0.723000539 -0.531356363
## [126] -1.714215614 0.391792128 0.368029305 1.999123924 -0.898521648
## [131] -0.563168214 1.219316346 -0.246307081 0.025208919 -0.470383839
## [136] 1.095440894 -0.787094905 -0.818131412 -1.013672772 0.704544618
## [141] -1.097532731 0.075921207 2.002525434 -0.148144181 0.148066874
## [146] 0.416029025 -0.813649876 -0.049246864 -1.144862836 1.077223715
## [151] -0.444647412 0.318448201 -1.174078079 -0.499986754 -0.558065949
## [156] -1.841881385 -0.435376251 1.017388058 0.576123966 -0.574589194
## [161] -0.851186996 -0.148453410 0.539744178 -0.411695282 1.181733751
## [166] 1.082019025 0.646775788 -1.887565304 0.072161583 1.633234206
## [171] -0.575221293 -1.119165063 -1.059624992 0.103341335 1.607363629
## [176] -1.245471140 -1.292532943 -0.459899638 -0.146751518 -0.671875569
## [181] -0.350567007 -0.199172518 0.315874331 0.557349722 -1.023438472
## [186] 0.618831564 0.635689048 -0.793575055 0.718537194 1.412158781
## [191] 0.485820237 -1.166795300 0.017098500 -1.059624992 -1.722246452
## [196] -1.579328455 -0.614113560 0.044344688 -1.017131126 0.843410817
## [201] -1.655407686 -1.539588084 1.550693014 0.303193701 -1.314901965
## [206] 0.215821956 0.965001163 0.128834472 1.349458216 -0.503891897
## [211] -0.585723683 1.221894763 0.618831564 0.602699401 0.002944489
## [216] -0.928712325 -0.518361958 -0.765689947 1.169064490 0.303193701
## [221] 0.185068529 -0.605546120 1.666958269 -1.178509592 -2.060314728
## [226] -0.506672677 -1.630337465 1.527196218 0.197455847 -0.942577572
## [231] 0.126520945 1.924254320 -0.784802978 -0.701311365 0.658133104
## [236] 0.473290811 -1.163625711 -1.161972705 -0.365574806 0.268289568
## [241] 0.056523959 0.428574367 0.083979330 -1.163325578 0.481693405
## [246] -0.651687060 -0.561553861 -0.943891791 -1.639655238 -0.235675088
## [251] -1.116166004 -0.989666660 -0.207998028 -1.394550964 0.884067504
## [256] -1.130397322 -0.465604444 0.175270998 -0.816103238 0.286017894
## [261] 0.624120275 0.315793613 -0.811946848 -0.037225618 1.229841473
## [266] 0.525726591 0.727079623 -0.398657676 -0.482896212 1.591693035
## [271] -0.823597475 -0.341470923 1.235894160 1.679673005 0.677349590
## [276] -0.682941845 1.244475243 -0.559944056 -0.310732275 0.059512786
## [281] 0.441777956 -0.247332537 0.297911811 0.745437774 0.757611360
## [286] 0.901618478 1.454463927 0.541249392 -0.018092123 -0.764664492
## [291] -0.222325980 1.637308742 -1.242156031 -0.816529564 -1.057080681
## [296] -0.634472599 -0.306399670 1.023568075 1.036178219 0.019622348
## [301] -0.760367129 0.976890533 -1.558373697 -1.361340765 0.457519036
## [306] -0.710340373 1.298908501 -0.004934009 1.137527761 0.036153551
## [311] 0.222952394 -0.270114242 -0.504326181 -1.484872882 0.664797426
## [316] 1.082019025 -0.007687504 -0.146210368 1.871903805 0.415778914
## [321] -1.831958798 -0.011666543 1.091545982 1.417363364 -1.972748578
## [326] -0.390471087 1.051080289 0.245913725 -1.248135959 -0.051085181
## [331] -1.279242952 -1.898124538 0.339282451 1.192099717 0.562988589
## [336] -0.001950866 0.596289738 0.933787305 0.661461854 -0.075538082
## [341] -0.453785560 1.282542144 -0.054685643 0.490991852 -0.841555448
## [346] -0.377788183 -0.630174100 0.901848125 0.246543550 0.481863935
## [351] 0.080524387 1.135922503 -0.694188884 -0.945324246 0.514428393
## [356] -0.648474270 1.243813585 0.546481260 0.438069492 0.198861017
## [361] -0.250962557 0.544617933 -0.824670678 0.288887350 0.828438260
## [366] -0.624957011 0.345528406 0.241972202 -0.672066562 0.456840326
## [371] -1.323667220 0.331593810 1.543353392 0.110266001 -0.283308736
## [376] -0.927066139 -0.050472408 0.640940243 1.670032361 0.062577783
## [381] -0.861452918 0.468846793 -0.249067398 1.213065843 2.077213139
## [386] -0.692048161 0.612820941 -1.145451733 0.919217200 -0.518537036
## [391] -1.147075182 -1.292532943 1.322750904 1.164680725 -0.221698429
## [396] 0.330301191 -0.259814215 1.519870239 -1.200078259 -1.217226782
## [401] 0.824240942 0.801251190 -1.025766778 0.599583245 1.651505954
## [406] -1.109347068 -1.024729954 -0.559853106 0.502675448 0.562540663
## [411] -0.266784355 0.595284746 -1.409057404 0.249619916 -0.317966169
## [416] -0.965246727 -0.580282631 -1.273197086 0.464495997 -1.405967396
## [421] -0.500160695 -0.259576609 0.247648586 -0.702389116 -0.339282451
## [426] 0.031407126 -1.472094482 0.363449999 -0.155263251 1.075038654
## [431] -0.904492481 -0.297911811 0.165182428 -1.070279723 -1.190078365
## [436] 0.006310756 -0.139641543 0.793365871 -0.998443284 1.102296210
## [441] -0.118890284 0.264168420 -0.365492951 -0.139023086 -0.783657015
## [446] 1.268222150 -0.248988954 -0.711620487 0.851407549 -0.920736056
## [451] -1.141627308 0.834816092 0.084977501 0.043426098 0.362713308
## [456] -0.272336820 -0.174184152 0.037531436 -1.386501935 0.815462045
## [461] -0.586539954 1.288310614 0.467480277 -0.472264219 0.696234110
## [466] -0.439416681 0.478001994 0.157276645 -0.353904852 -1.373027771
## [471] -1.750927368 0.635594688 0.431595026 0.115423973 1.160769898
## [476] 1.034738943 -0.271304543 -0.940076461 -1.146779596 -0.314828412
## [481] 0.681588972 -1.257019449 -1.606531441 -1.383309609 0.828006250
## [486] -0.582366511 -0.181489668 -0.088894012 -0.282910833 -0.834384082
## [491] -0.535501385 0.878765150 0.853606252 -0.498166628 -0.252462087
## [496] 1.265493665 1.610155778 -0.805264335 -0.508413223 -0.828438260
## [501] -0.934614945 0.212925215 -0.357163117 1.369307938 0.419952357
## [506] -1.608200364 0.518712113 -0.080141263 1.451608114 0.626073415
## [511] -0.108265112 -1.931121005 0.399320470 1.079001777 -1.312000677
## [516] 1.144126145 1.141188477 1.578791853 0.953007202 -0.291041715
## [521] 0.512334282 0.152940629 0.543375336 0.331109504 0.547281616
## [526] 0.722006916 -0.558333113 0.221306209 1.844391591 -1.196940502
## [531] 1.920852810 0.343742386 -0.402801561 1.499074642 1.031087322
## [536] -0.754455414 0.340741053 0.483669282 -0.158670446 -0.022530457
## [541] 0.087663921 -0.581821951 -1.131122644 1.417156454 -0.004781668
## [546] -1.189766863 0.494360393 1.152409368 -1.840626283 -0.285698434
## [551] -0.650929906 -0.435628635 -0.013578756 -1.073540261 1.596326911
## [556] -0.611621545 -0.014726993 2.016931830 -1.575344868 0.458284148
## [561] 1.498133315 -0.352113148 1.599341886 -0.960503712 0.421623554
## [566] 0.167508460 -0.071241857 -0.670725058 0.750800382 -0.717843704
## [571] -1.204016371 -0.853497113 -0.004704361 0.209952304 0.484701559
## [576] 0.117427135 0.682362042 -0.845047907 0.475773732 -0.699162683
## [581] -0.542223688 -0.001339231 -0.653579946 -0.313382316 0.014649686
## [586] 0.803045168 0.889053808 0.193635969 0.873824320 1.674679879
## [591] -0.727777660 0.510939344 0.751308562 0.592913239 -0.280761014
## [596] 1.136943411 -0.567924872 -0.649417871 -1.112748578 -0.600407475
## [601] 0.894633558 1.144421731 -1.312723725 0.257520014 0.933905540
## [606] 0.447266757 1.317266651 1.223995696 0.818345143 -0.180011739
## [611] 0.921086212 -1.931121005 -1.103421710 0.252462087 0.006846221
## [616] 0.926243047 0.837312655 0.544883960 -0.176747790 0.522040864
## [621] -0.020464768 -0.414861461 1.521812010 0.065260792 0.771856321
## [626] 1.114883617 1.767461981 -0.550394361 -0.632882120 1.123758011
## [631] -0.763741355 -0.379843641 1.046571469 -0.538240101 -1.460439307
## [636] -0.945565262 1.572702786 0.649985168 -0.715074293 -0.099266799
## [641] -0.280442691 -0.801460374 -0.437817107 -1.061773673 -0.621613481
## [646] 1.245139174 1.383907602 1.833595888 -0.701703584 0.196052952
## [651] -0.830921181 0.553154678 0.195661869 0.490647381 -0.367701887
## [656] -1.723597052 0.731070031 1.583330231 -0.137015377 0.788763828
## [661] 0.362224455 -1.735888873 1.780745151 0.177758466 -0.735976755
## [666] 1.059088390 -0.005852598 0.109957909 0.810778147 0.314828412
## [671] 0.202606998 0.149614152 -0.604443358 -1.794360287 -1.049620550
## [676] 0.217858087 -0.691077275 1.179889750 -0.643667590 1.929638529
## [681] 1.653602340 -0.629333954 -1.221894763 -0.037455266 0.320300160
## [686] -0.095346877 0.385522299 1.780745151 -0.161537628 -0.283388317
## [691] 0.994423317 0.271543286 -1.675612111 0.515301508 0.086051841
## [696] 1.233433977 0.894176537 0.001950866 -1.315083864 0.253805865
## [701] 0.589177489 1.703670023 -0.097345492 -0.792003902 -1.525968401
## [706] 0.016868853 -0.048787570 0.269637894 -0.405541414 0.981833637
## [711] 1.468711162 -1.841463018 0.960988018 -0.358795660 -1.218031684
## [716] -0.064341066 0.338147856 0.741403028 0.109650955 1.610433173
## [721] -0.190441369 -0.611253199 0.339848611 -0.259022954 0.607384436
## [726] -1.564849299 -0.719725222 0.093963308 0.458539944 -0.796408131
## [731] 0.511723783 1.898124538 2.005945134 -1.205280569 0.834384082
## [736] 0.544617933 0.175039077 1.224805146 0.315633315 -0.275433649
## [741] -1.114312909 1.018670446 0.288009687 -0.616424813 -0.202919637
## [746] 0.564691618 1.176827027 0.770414772 -1.167400114 -0.668331950
## [751] -1.280457127 0.424302016 1.190855983 -1.626017365 0.526165422
## [756] 0.488577143 0.866230039 -1.443754627 0.462962362 0.205653805
## [761] 0.873599220 -1.745984264 -1.874996087 -0.717545845 -1.565108505
## [766] 1.130397322 -0.682264272 0.051927600 -0.379595804 -2.020451575
## [771] -0.780230494 1.317084752 1.979215085 -0.177446964 0.087511580
## [776] -0.783138603 0.351706149 -1.578528099 -0.590451918 1.190855983
## [781] 0.667375843 -0.101034630 -1.252315087 0.916652425 -0.430839009
## [786] 1.977587090 1.495322977 0.177835773 0.113421947 0.062807430
## [791] -0.700529199 1.607922968 -1.045646059 1.944117685 0.362877017
## [796] -1.731077646 1.140895165 0.814823125 -0.593643108 1.598245944
## [801] 0.276149876 1.216908458 0.112497673 -0.571344572 -0.360590775
## [806] -0.095423047 0.609961717 1.212108600 -0.894176537 -0.050854396
## [811] -0.678601282 -1.476400939 0.748875664 0.739491952 0.099189492
## [816] 0.107726237 0.309207735 0.667375843 0.144277692 1.628891368
## [821] 1.090713795 0.706310175 1.324035566 -2.057122401 0.524496500
## [826] -1.551456990 0.245754563 -0.337823849 -0.054302518 -0.237799895
## [831] -0.210734470 1.221087587 -0.327797807 -0.582638222 1.565890670
## [836] 0.850308197 0.527484190 0.642162377 -0.988545708 -0.498773716
## [841] 1.159571639 1.217067620 0.630548129 1.159271505 1.797043296
## [846] 1.937078196 1.129819793 -1.030307430 1.141188477 -1.224320840
## [851] 0.929771886 -0.022760105 -0.920967977 0.325619567 -1.840212462
## [856] -1.145895112 0.146442289 -1.734169928 1.127937139 1.598518793
## [861] 1.083117240 0.393114306 -2.027572918 1.309292657 0.828331395
## [866] 0.739792085 -0.029724561 -1.515272743 -0.662128059 0.143813850
## [871] -0.775364697 -0.679854111 -0.698967142 0.012125838 -0.352845291
## [876] -0.449549589 -0.110496785 0.075231128 -1.062444426 -1.128082658
## [881] -0.081753342 0.516874934 -0.320621893 0.107341975 0.169991381
## [886] 0.186001898 1.080097718 -1.380726644 -0.957472821 0.609777544
## [891] -0.908762559 0.506238393 0.246623131 0.441862085 -0.795778305
## [896] 1.122893991 -0.720121989 -1.419034561 -1.256514679 -0.476973128
## [901] 0.264089977 -1.242819962 0.128063675 1.243813585 0.960624220
## [906] 0.372125442 -1.423445610 -0.940908649 0.686422936 -0.879665549
## [911] 1.628313839 0.360264494 0.346665274 -0.381241989 0.534265610
## [916] 0.009371206 0.047562025 -0.474317403 -1.090020305 -0.857910436
## [921] 1.560697456 -1.030828116 0.856143743 -0.138714995 0.086896534
## [926] -1.426401468 -1.612957021 -1.262942533 -0.114577006 0.490560979
## [931] -1.476173566 0.075997377 0.157585873 1.562771104 1.128514668
## [936] 0.259497028 -0.561017259 0.099881845 -0.101957767 -0.419869366
## [941] 0.196598648 -1.130108558 0.130609124 -0.258311275 -0.151702579
## [946] -1.224805146 1.415487532 -0.766715402 -1.312364475 -1.391722435
## [951] -0.325619567 0.748570983 0.727179668 1.324956429min(Rango_2)## [1] -2.060315max(Rango_2)## [1] 2.077213