# Simulate k random samples of size n from the 
# statandard normal distribution.  Plot the first values
# versus the last values.  Then plot the simulated
# joint distribution of the min and the max.

# See the last formula from the notes on Order Statistics 
# for the formula.

n <- 5
k <- 1000

x <- matrix(rnorm(n*k),nrow=k)
x[1:3,]

x.order <- t(apply(x,1, sort))
x.order[1:3,]

plot(x[,1],x[,n])

plot(x.order[,1],x.order[,2])