9

## PREGUNTA 9

## b) Simulación con variable de control
## Y=U (variable de control)
rm(list = ls())

n <- 100
X <- vector()
U <- vector()
med_Y=0.5

for(i in 1:n)
{
  U[i]=runif(1,0,1) #variable  de control
  X[i]=exp((U[i])^2)
}
c=-cov(X,U)/var(X)
p=cor(U,X)
Var_IC=var(U)*(1-p^2)
Var_IC

## c) Variable antiteticas

rm(list = ls())
X=vector()
U=vector()
n=100

for (i in 1:n) {
  U[i]=runif(1,0,1)
  X[i]=(exp(U[i]^2)+(exp((1-U[i])^2)))/2
}
var(X)/n