Let (X,Y) be jointly uniformly distributed over the unit square with coordinates (0,0), (1,0), (0,1) and (1,1).
a. What is the value of the joint pdf, f_{X,Y}(x,y), inside the square?
b. Find the marginal pdf of X.
c. Are X and Y independent? Justify your answer.
d. Find the pdf of Z = max(X, Y).
e. Let W = X + Y. Find f_{W|X}(w|x).