Let X and Y have the joint pmf f(x, y) = x + y 32 , x = 1, 2, y = 1, 2, 3, 4. (a)

QUESTION:

Let X and Y have the joint pmf f(x, y) = x + y 32 , x = 1, 2, y = 1, 2, 3, 4. (a) Display the joint pmf and the marginal pmfs on a graph like Figure 4.3-1(a). (b) Find g(x | y) and draw a figure like Figure 4.3-1(b), depicting the conditional pmfs for y = 1, 2, 3, and 4. (c) Find h(y | x) and draw a figure like Figure 4.3-1(c), depicting the conditional pmfs for x = 1 and 2. (d) Find P(1 Y 3 | X = 1), P(Y 2 | X = 2), and P(X = 2 | Y = 3). (e) Find E(Y | X = 1) and Var(Y | X = 1).