sampling.dist.1<-NULL
for(sample.count in 1:10000){
  set.seed(sample.count)
  sample.mean.1<-mean(rnorm(2,2.5,1.118))
  sampling.dist.1<-c(sampling.dist.1, sample.mean.1)
}
mean(sampling.dist.1)
var(sampling.dist.1)
table(round(sampling.dist.1))

sampling.dist.2<-NULL
for(sample.count in 1:10000){
  set.seed(sample.count)
  sample.mean.2<-mean(rnorm(5,2.5,1.118))
  sampling.dist.2<-c(sampling.dist.2, sample.mean.2)
}
mean(sampling.dist.2)
var(sampling.dist.2)
table(round(sampling.dist.2))

sampling.dist.3<-NULL
for(sample.count in 1:10000){
  set.seed(sample.count)
  sample.mean.3<-mean(rnorm(10,2.5,1.118))
  sampling.dist.3<-c(sampling.dist.3, sample.mean.3)
}
mean(sampling.dist.3)
var(sampling.dist.3)
table(round(sampling.dist.3))

sampling.dist.4<-NULL
for(sample.count in 1:10000){
  set.seed(sample.count)
  sample.mean.4<-mean(rnorm(30,2.5,1.118))
  sampling.dist.4<-c(sampling.dist.4, sample.mean.4)
}
mean(sampling.dist.4)
var(sampling.dist.4)
table(round(sampling.dist.4))

par(mfrow=c(2,2))

hist(sampling.dist.1,  freq=F, col="grey", xlab="", xlim=c(-1, 6), breaks=100)
par(new=T)
plot(density(sampling.dist.1), axes=F, main="", xlim=c(-1, 6), lwd=2, col="blue")

hist(sampling.dist.2,  freq=F, col="grey", xlab="", xlim=c(-1, 6), breaks=100)
par(new=T)
plot(density(sampling.dist.2), axes=F, main="", xlim=c(-1, 6), lwd=2, col="blue")

hist(sampling.dist.3,  freq=F, col="grey", xlab="", xlim=c(-1, 6), breaks=100)
par(new=T)
plot(density(sampling.dist.3), axes=F, main="", xlim=c(-1, 6), lwd=2, col="blue")

hist(sampling.dist.4,  freq=F, col="grey", xlab="", xlim=c(-1, 6), breaks=100)
par(new=T)
plot(density(sampling.dist.4), axes=F, main="", xlim=c(-1, 6), lwd=2, col="blue")