Question

Q: Assistance in understanding and solving this example from Probability and Statistical (Conditional Distributions) with the steps of the solution to better understand, thanks.

**Please give the step by steps with details to completely see how the solution came about.

1) Let X and Y have the joint pmf:   f(x,y) = (x+2y)/33,   x = 1,2   y = 1,2,3.

a) Display the joint pmf and the marginal pmfs on a graph.

b) Find g(x $\mid$ y) and draw a figure depicting the conditional pmfs for y = 1,2,3.

c) Find h(x $\mid$ y) and draw a figure depicting the conditional pmfs for x = 1 and 2.

d) Find P(1 $\leq$ Y $\leq$ 3 $\mid$ X = 1), P(Y $\leq$ 2 $\mid$ X = 2), and P(X = 2 $\mid$ Y = 3).

e) Find E(Y $\mid$ X = 1) and Var(Y $\mid$ X =1).

Answer 1