Suppose that two-dimensional continuous random variable (X, Y) has joint probability density function given by
f(x,y) = 24xy, x is less than equal to 1 and greater than equal to 0, y is less than equal to 1 and greater than equal to 0, x+y is less than equal to 1 and greater than equal to 0.
Check that E(Y) = E[E(Y|X)] and V(Y) = E[V(Y|X)] + V[E(Y|X)].