A what is the probability model for random variables a and

Question

The probability model for random variable A is

The conditional probability model for random variable B given A is:

(a) What is the probability model for random variables A and B? Write the joint PMF P_A,B(a, b) as a table.

(b) If A = 1, what is the conditional expected value E[B|A = 1]?

(c) If B = 1, what is the conditional PMF P_A|B (a|1)?

(d) If B = 1, what is the conditional variance Var[A|B = 1] of A?

(e) What is the covariance Cov[A, B] of A and B?