# R code to approximate expected values of fcns of r.v.'s
# Examples 3 and 4

# Example 3

my.n <- 1000

rand.norm <- rnorm(my.n, 10, 1)

expect.val.1 <- (1/my.n)*sum(rand.norm^2)

print(expect.val.1)


# Example 4

# A plot of the beta(5,1) density:

X <- seq(0.01,0.99,by=0.01)
plot(X,dbeta(X,5,1), ylab="Density",type="l")

my.n <- 1000

rand.beta <- rbeta(my.n, 5, 1)

expect.val.2 <- (1/my.n)*sum(-log(rand.beta))

print(expect.val.2)