Question: Suppose that a point (X, Y) is chosen according to the uniform distribution on the triangle with vertices (0, 0), (0, 1), (1, 0). Calculate:
a) the mean and variance of X:
b) the conditional mean and variance of X given that Y = 1/3:
c) the mean and variance of max (X, Y):
d) the mean and variance of min (X, Y).