## function to simulate data for different sample sizes, plot esimtated variance and compare to expected value

## reset plot area from exercise 1
par(mfrow=c(1,1))
plot(c(0,32), c(0,15), type="n", xlab="Sample size", ylab="Variance", main="Sample size simulation")

for(df in seq(3,31,2)){
for(i in 1:30){
x <- rnorm(df, mean=10, sd=2)
points(df, var(x)) }}

abline(4,0, col="red")