#sampling distribution of sample mean of 1000 samples with 11 size samples from normal dist. 

set.seed(23456789)

sample_size <- 11

n_rep <- 1000

sample_mean <- rep(NA, n_rep)
sample_var <- rep(NA, n_rep)

#graphics.off()
#par(mfrow=c(1,2))

for (i in 1:n_rep) {
     my_sample <- rnorm(sample_size,10,2) 
     sample_mean[i] <- mean(my_sample)
     sample_var[i] <- var(my_sample)
   }

(mean(sample_var))
(var(sample_var))

hist(sample_var, breaks=40, prob=T, main=paste( "samples of size 11" ),col="black")
par(new=T)
plot(density(sample_var), xlab="", axes=F, main="", col="blue")