Suppose that the joint distribution of X and F is represented by the following table:

1 X 2 3

graph the joint PMF of X and Y (you will need a three-dimensional graph)

are X and Y independent? Explain your answer, determine the marginal distributions of X and Y determine the conditional distribution of X given that Y = 2. What does this tell you about the conditional distribution of X given any particular value of F?

find E{X), E(Y),E(X+ Y), E(XY), and E(4X- 2F)

find cov (X, F), var (X + F), and var (X — F)

using the distribution obtained in (d), find E(X | F = 2).

(a)

(b)

(c)

(d)

(e)

(f)

(g)

F 1 2 3 4

.12 .18 .24 .05

.06 .09 .12 .03

.02 o

CO

.04 .01