Problem 5.67 Let the random vector (X, Y ) have the joint density function f(x, y) = xe−xy−x, for x > 0,y> 0) f(x, y)=0, elsewhere. Compute:

(a) f(y|x).

(b) µY |x. Problem 5.68 Let X and Y have a bivariate normal distribution with parameters µX = 2, µY = 1, σ2 X = 9, σ2 Y = 16, ρ = 3/4. Compute:

(a) P(Y < 1)

(b) P(Y < 1|X = 0)

(c) E(Y |X = 0)

(d) V (X + Y )