The joint probability density function of two discrete random variables X and Y is given by the following table:
Y
1 3 9
2 1/8 1/24 1/12
X 4 1/4 1/4 0
6 1/8 1/24 1/12
(a) Find the marginal probability density function of Y
(b) Find the conditional probability density function of Y given that X=2
(c) Find the covariance of X and Y
(d) Are X and Y independent?