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!
Hi harish21,
Thanks very much for the reply. So I can finish letter b thanks to your hint. Would you mind explaining the intuition of letter a? Specifically, could you talk about why
P[Z≤z] = P[(X≤z)∩(Y≤z)]
I just want to develop a better understanding of the problem. Thank you.
I work with order statistics all the time.
I can google my name and find some of my papers...
http://w3.math.sinica.edu.tw/bulleti...d322/32203.pdf