41. The joint probability mass function of X and Y is given by

$$

p(1, 1) = \frac{1}{8}

$$

$$

p(1, 2) = \frac{1}{4}

$$

$$

p(2, 1) = \frac{1}{8}

$$

$$

p(2, 2) = \frac{1}{4}

$$

(a) Compute the conditional mass function of X given Y = i, i = 1, 2.

(b) Are X and Y independent?

(c) Compute P(XY ≤ 3), P(X + Y > 2), P(X/Y > 1).