Parcial 2

##pregunta 1

#pregunta a

comision.1 <- choose(12,3)*choose(8,4)
comision.1

## [1] 15400

#pregunta b

p.comision.total<-choose(20,7)
p.comision<-comision.1/p.comision.total
p.comision

## [1] 0.1986584

##pregunta 2

#pregunta a

f.2 <- function(x){2*(x+2)/5}
f.integ2 <- integrate(f.2, lower=0, upper=1)$value
f.integ2

## [1] 1

#pregunta b
f.integb <- integrate(f.2,lower = 0.25,upper=0.5)$value
f.integb

## [1] 0.2375

##pregunta 3

nombres_filas <- c("a1","a2","a3","total")
def <- c(0.009,0.09,0.0025,sum(0.009,0.09,0.0025))
defc <- c(0.441,0.291,0.2475,sum(0.441,0.291,0.2475))
total <- c(0.45,0.30,0.25,sum(0.45,0.30,0.25))
tabla <- data.frame(nombres_filas,def,defc,total)
tabla

##   nombres_filas    def   defc total
## 1            a1 0.0090 0.4410  0.45
## 2            a2 0.0900 0.2910  0.30
## 3            a3 0.0025 0.2475  0.25
## 4         total 0.1015 0.9795  1.00

tabla$def[2]

## [1] 0.09

##pregunta 4

x <- c(2,3,4,5,6)
f.x <- c(0.01,0.25,0.4,0.3,0.04)

esperanza <- sum(x*f.x)
varianza <- sum(((x-esperanza)^2)*f.x)
varianza

## [1] 0.7379

##pregunta 5

size <- 1000
media <- 164.5
desv.estatura <- 7

#pregunta a

p.a <- pnorm(168.5,media,desv.estatura)-pnorm(160.5,media,desv.estatura)
p.a

## [1] 0.4322908

#pregunta b
p.b <- pnorm(168.5,media,desv.estatura,F)
p.b

## [1] 0.2838546

#pregunta c
q.c <- qnorm(0.015,media,desv.estatura,F)
q.c

## [1] 179.6906