Answer and explain the following question.

Problem 7 Consider two discrete random variables X and Y with the joint PMF given in the following table: Y =1 Y =2 X =1 12 X =2 0 X =4 12 Co / M a. Find P(X 1). b. Find the marginal PMFs of X and Y. c. Find P(Y = 2 | X = 1). d. Are X and Y independent? e. Let Z = X - 2Y, find the PMF of Z. f. Find P(X = 2 | Z = 0). g. Find the conditional PMF of X, given Y = 1, i.e., Pxjy (x|1)