set.seed(123456)

par(mfrow=c(2,2))

vbar10<-numeric(10000)

for(j in 1:10000) {
  sample<-rnorm(10,10,2)
  vbar10[j] <-var(sample)
}

(mean(vbar10))
(var(vbar10))

hist(vbar10, freq=F, xlab="", breaks=100)
par(new=T)
plot(density(vbar10), axes=F, main="", col="blue")

vbar20<-numeric(10000)

for(j in 1:10000) {
  sample<-rnorm(20,10,2)
  vbar20[j] <-var(sample)
}

(mean(vbar20))
(var(vbar20))

hist(vbar20, freq=F, xlab="", breaks=100)
par(new=T)
plot(density(vbar20), axes=F, main="", col="blue")

vbar30<-numeric(10000)

for(j in 1:10000) {
  sample<-rnorm(30,10,2)
  vbar30[j] <-var(sample)
}

(mean(vbar30))
(var(vbar30))

hist(vbar30, freq=F, xlab="", breaks=100)
par(new=T)
plot(density(vbar30), axes=F, main="", col="blue")

vbar100<-numeric(10000)

for(j in 1:10000) {
  sample<-rnorm(100,10,2)
  vbar100[j] <-var(sample)
}

(mean(vbar100))
(var(vbar100))

hist(vbar100, freq=F, xlab="", breaks=100)
par(new=T)
plot(density(vbar100), axes=F, main="", col="blue")