PROBLEM 2

Question

Let X and Y be independent random variables, with X uniformly distributed on [0,1] and Y uniformly distributed on [0,2]. Find the PDF fZ(z) of Z = max {X, Y}.

1. For z < 0 or z > 2:
fZ(z) = ????

2. For 0 <= z <= 1:
fZ(z) = ????

3. For 1 <= z <= 2:
fZ(z) = ????

Answer 1

1. 0
2. Z
3. 1/2