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].