Hi there,

I was wondering if someone could explain how to go about the following problem.

Let X and Y be independent random variables having distribution functions F_{x}and F_{Y}, respectively.

a) Define Z = max{X,Y} to be the larger of the two. Show that F_{Z}(z) = F_{X}(z)F_{Y}(z) for all z.

b) Define W = min{X,Y} to be the smaller of the two. Show that F_{W}(w) = 1 - [1-F_{X}(w)][1-F_{Y}(w)] for all w.

Thanks!