U2A6 Introduccion a la probabilidad frecuentista

Ejercicios Calcular la probabilidad de obtener un valor menor a 9 si tenemos media de 8 y desviacion estandar de 2

pnorm(9, mean = 8, sd=2)
## [1] 0.6914625

Generar 150 numeros aletorios de media 5 y desviacion de 0.5.

x <- rnorm(150, mean = 5, sd=0.5)
x
##   [1] 4.498655 4.913228 5.254584 5.017711 4.804661 5.566273 5.785748 5.053153
##   [9] 4.970805 5.609627 5.391927 5.451550 5.482381 5.073738 4.979722 4.519463
##  [17] 4.105951 5.522372 6.406492 4.783764 4.617050 4.196692 4.630263 4.950192
##  [25] 5.076133 5.119511 5.492932 5.499728 4.883555 5.565487 5.552619 5.069625
##  [33] 5.275747 6.210724 5.402257 5.136710 4.954046 4.185261 3.973837 4.430868
##  [41] 5.084574 5.498706 5.251188 5.112200 5.052909 4.905790 4.621036 4.649154
##  [49] 4.436863 3.934416 5.071284 4.892498 5.658089 4.975506 4.187472 4.315123
##  [57] 4.596336 4.610886 5.050017 4.552048 4.722760 4.822062 6.059989 4.997064
##  [65] 6.468266 3.979559 3.822504 5.603449 5.115554 4.841293 5.638565 4.571781
##  [73] 5.670878 5.457909 5.548947 5.412339 4.676819 4.991864 5.590764 5.228590
##  [81] 5.181286 4.774160 5.123667 3.813018 4.728782 5.372599 4.437582 4.655823
##  [89] 5.298762 6.223284 4.748198 5.547913 4.854588 4.411956 5.307541 4.344912
##  [97] 5.578701 6.000059 4.779390 4.765069 3.679470 5.508600 5.517737 4.870002
## [105] 5.619240 5.592528 4.720841 4.612852 5.436986 4.622091 5.302240 4.572248
## [113] 5.582744 5.151108 5.114240 4.699939 5.057679 5.133997 4.880818 5.601885
## [121] 5.923192 5.540027 5.180125 4.557773 4.348712 4.757516 5.283979 4.900742
## [129] 5.311198 4.612323 5.637001 4.976420 5.182915 5.514006 5.353152 5.687724
## [137] 4.669553 4.241770 5.001292 5.696648 4.380847 4.894896 4.957418 5.515732
## [145] 4.781367 5.485918 5.435134 5.207501 4.855838 5.155913

Obtener media, mediana, moda de los datos generados y grafico de caja y bigote

mean(x)
## [1] 5.049088
median(x)
## [1] 5.055416
library(modeest)
## Warning: package 'modeest' was built under R version 4.0.4
mfv(x)
##   [1] 3.679470 3.813018 3.822504 3.934416 3.973837 3.979559 4.105951 4.185261
##   [9] 4.187472 4.196692 4.241770 4.315123 4.344912 4.348712 4.380847 4.411956
##  [17] 4.430868 4.436863 4.437582 4.498655 4.519463 4.552048 4.557773 4.571781
##  [25] 4.572248 4.596336 4.610886 4.612323 4.612852 4.617050 4.621036 4.622091
##  [33] 4.630263 4.649154 4.655823 4.669553 4.676819 4.699939 4.720841 4.722760
##  [41] 4.728782 4.748198 4.757516 4.765069 4.774160 4.779390 4.781367 4.783764
##  [49] 4.804661 4.822062 4.841293 4.854588 4.855838 4.870002 4.880818 4.883555
##  [57] 4.892498 4.894896 4.900742 4.905790 4.913228 4.950192 4.954046 4.957418
##  [65] 4.970805 4.975506 4.976420 4.979722 4.991864 4.997064 5.001292 5.017711
##  [73] 5.050017 5.052909 5.053153 5.057679 5.069625 5.071284 5.073738 5.076133
##  [81] 5.084574 5.112200 5.114240 5.115554 5.119511 5.123667 5.133997 5.136710
##  [89] 5.151108 5.155913 5.180125 5.181286 5.182915 5.207501 5.228590 5.251188
##  [97] 5.254584 5.275747 5.283979 5.298762 5.302240 5.307541 5.311198 5.353152
## [105] 5.372599 5.391927 5.402257 5.412339 5.435134 5.436986 5.451550 5.457909
## [113] 5.482381 5.485918 5.492932 5.498706 5.499728 5.508600 5.514006 5.515732
## [121] 5.517737 5.522372 5.540027 5.547913 5.548947 5.552619 5.565487 5.566273
## [129] 5.578701 5.582744 5.590764 5.592528 5.601885 5.603449 5.609627 5.619240
## [137] 5.637001 5.638565 5.658089 5.670878 5.687724 5.696648 5.785748 5.923192
## [145] 6.000059 6.059989 6.210724 6.223284 6.406492 6.468266
boxplot(x)

hist(x, freq = FALSE)
curve(dnorm (x, mean = 5, sd=0.5), from = 1.5, to =6.5, add=TRUE)

Genere un conteo y calculo de probabilidad de 30 numeros de forma binomial

x <- rbinom(30,5,0.5)
x 
##  [1] 4 4 3 2 2 3 4 2 2 4 3 3 2 3 2 2 2 4 1 1 3 4 3 1 2 4 2 2 3 4