2.6. Let X and Y be independent random variables having distribution functions F, and F, respectively.

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

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