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] 5.086054 4.572658 5.199447 5.071598 5.221623 4.572002 5.743074 4.456640
##   [9] 5.180212 4.642860 4.885767 5.735122 4.425400 5.757053 5.248169 5.119300
##  [17] 4.250810 5.239415 5.066969 4.667115 5.109131 4.860830 5.410856 5.109025
##  [25] 4.973053 6.022944 4.812849 4.950305 4.230212 4.820337 4.634223 6.174620
##  [33] 4.659358 5.514074 5.273699 4.967045 4.859656 4.096137 4.617601 4.952555
##  [41] 5.224532 5.205993 3.991682 5.138308 5.247949 4.770870 4.704189 4.207992
##  [49] 5.226068 5.871193 4.344373 4.421659 5.587809 5.106089 4.700860 5.255613
##  [57] 4.686728 4.924193 4.631846 4.458585 5.126923 5.087377 4.659297 4.744032
##  [65] 5.040669 5.154179 5.544374 4.792969 5.398341 5.298890 5.213425 4.312716
##  [73] 3.739962 6.123419 5.514736 5.151921 4.716604 5.833544 5.074337 5.064258
##  [81] 4.713316 4.178680 4.812621 4.632695 4.553514 4.449009 5.263536 5.302035
##  [89] 4.959954 5.111138 4.939220 5.121204 5.739902 4.163144 5.102921 5.159547
##  [97] 4.967917 4.527071 5.331066 5.428050 5.075448 5.060728 4.139841 5.723020
## [105] 5.420765 4.790507 4.469521 3.607183 5.524231 4.775566 5.496550 6.085658
## [113] 4.660287 4.834719 4.668734 5.431816 5.188497 3.815728 5.262123 4.872303
## [121] 5.947195 4.651700 4.408225 5.066703 5.261563 4.168686 5.509496 4.964117
## [129] 4.913479 4.437910 5.111971 5.048568 4.252801 4.709369 4.006343 4.704419
## [137] 5.359972 5.203828 5.155652 5.255767 4.619325 4.564816 5.056809 5.358192
## [145] 5.868477 5.995531 5.023731 3.857010 4.793207 5.045423

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

mean(x)
## [1] 4.967789
median(x)
## [1] 5.043046
library(modeest)
mfv(x)
##   [1] 3.607183 3.739962 3.815728 3.857010 3.991682 4.006343 4.096137 4.139841
##   [9] 4.163144 4.168686 4.178680 4.207992 4.230212 4.250810 4.252801 4.312716
##  [17] 4.344373 4.408225 4.421659 4.425400 4.437910 4.449009 4.456640 4.458585
##  [25] 4.469521 4.527071 4.553514 4.564816 4.572002 4.572658 4.617601 4.619325
##  [33] 4.631846 4.632695 4.634223 4.642860 4.651700 4.659297 4.659358 4.660287
##  [41] 4.667115 4.668734 4.686728 4.700860 4.704189 4.704419 4.709369 4.713316
##  [49] 4.716604 4.744032 4.770870 4.775566 4.790507 4.792969 4.793207 4.812621
##  [57] 4.812849 4.820337 4.834719 4.859656 4.860830 4.872303 4.885767 4.913479
##  [65] 4.924193 4.939220 4.950305 4.952555 4.959954 4.964117 4.967045 4.967917
##  [73] 4.973053 5.023731 5.040669 5.045423 5.048568 5.056809 5.060728 5.064258
##  [81] 5.066703 5.066969 5.071598 5.074337 5.075448 5.086054 5.087377 5.102921
##  [89] 5.106089 5.109025 5.109131 5.111138 5.111971 5.119300 5.121204 5.126923
##  [97] 5.138308 5.151921 5.154179 5.155652 5.159547 5.180212 5.188497 5.199447
## [105] 5.203828 5.205993 5.213425 5.221623 5.224532 5.226068 5.239415 5.247949
## [113] 5.248169 5.255613 5.255767 5.261563 5.262123 5.263536 5.273699 5.298890
## [121] 5.302035 5.331066 5.358192 5.359972 5.398341 5.410856 5.420765 5.428050
## [129] 5.431816 5.496550 5.509496 5.514074 5.514736 5.524231 5.544374 5.587809
## [137] 5.723020 5.735122 5.739902 5.743074 5.757053 5.833544 5.868477 5.871193
## [145] 5.947195 5.995531 6.022944 6.085658 6.123419 6.174620
boxplot(x)

De los datos generados obtener histograma de frecuencia absolutas e histograma con curva de distribuccion normal superpuesta

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] 1 1 3 2 3 1 2 2 3 3 4 0 3 2 5 0 4 2 3 2 3 3 3 2 4 4 1 3 1 4
table(x)
## x
##  0  1  2  3  4  5 
##  2  5  7 10  5  1