Question

a) Use the following R code to empirically check the Central Limit Theorem via simulation

.n <- 40 # sample size

m <- c(1:200) #create a vector of length 200

for (i in 1:200) { #simulate 200 samples

x <- rnorm(n)

m[i] <- mean(x) }

hist(m)

b) Repeat part (a) with n=200 and compare the histograms. Describe what you observe and what you expect when n increases.

c) Repeat parts (a) and (b) with runif() and rexp() respectively instead of rnorm(). Compare with the case using rnorm().

Answer 1