Suppose that the random variables X and Y have a joint probability density function f(x, y) =

Question:

Suppose that the random variables X and Y have a joint probability density function
f(x, y) = 4x(2 - y)
for 0 ≤ x ≤ 1 and 1 ≤ y ≤ 2.
(a) What is the marginal probability density function of X?
(b) Are the random variables X and Y independent?
(c) What is Cov(X, Y)?
(d) What is the probability density function of X conditional on Y = 1.5?