Question: B.5 The joint probability density function of two discrete random variables X and Y is given by the following table; Y 1 3 9 2

B.5 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?

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