Consider random variables X and Y with a joint pmf, given in the following table.

X/ Y 0 1 2 3

0 0 0.05 0.0625 0.02

1 0.125 0.25 0.02 0

2 0.03 0.05 0 0.125

3 0.1 0.0625 0.055 0.05

a. Compute pX(x) and pY(x), namely the marginal pmf of X and Y.

b. Compute the mean, variance, and squared coefficient of variation of X.

c. Are X and Y independent?

d. Compute the conditional expectations E[X|Y = 1] and E[X|Y > 1].

e. Compute the conditional expectation E[X+2Y|X > 1, Y < 2].