Suppose the joint probability density function of X and Y is uniform in the plane square with corners (0,0), (0,3), (3,0) and (3,3).
a) Plot the joint p.d.f.
b) Find the probability of X + Y < 3
c) Find the probability of X > 1/2
d) Find the probability of X > 1 or Y > 1
e) Find the probability of X + Y < 3/2