10-12

#### PREGUNTA N°10
## a)
rm(list = ls())
Y2=vector()
U=vector()
n=100

for (i in 1:n) {
 U[i]=runif(1,0,1) #Variable de control
Y2[i]=(exp((U[i]+U[i])^2))
}
c=-cov(Y2,U)/var(U)
p=cor(U,Y2);p
Var_IC=var(U)*(1-p^2)
Var_IC

#### b)antiteticas
rm(list = ls())

Y2=vector()
U=vector()

n=100

for (i in 1:n) {
  U[i]=runif(1,0,1)
  Y2[i]=(exp((2*U[i])^2)+(exp((1-2*U[i])^2)))/2

}

var(Y2)/n

#### Pregunta 12
## a)

n <- 10000
x <- runif(n, -1, 1)
y <- runif(n, -1, 1)
indice <- (x+y < 0)
# Aproximación por simulación
sum(indice)/n