The joint probability distribution of variables X and Y is shown in the table below, where X is the number of tennis racquets and Y is the number of golf clubs sold daily in a small sports store.
Y

1

2

3

1

0.30

0.18

0.12

2

0.15

0.09

0.06

3

0.05

0.03

0.02

a. a. find out E(XY)
b. Find out the marginal probability distributions of X and Y.
c. Are X and Y independent? Describe.
d. Compute the conditional probability P(Y = 2  X = 1)
e. Compute the expected values of X and Y.
f. Compute the variances of X and Y.
g. Compute Cov(X,Y). Did you expect this answer? Why?
h. Find the probability distribution of the random variable X + Y.
i. Compute E(X + Y) and Var(X + Y) directly by using the probability distribution of X + Y .
j. Show that Var(X + Y) = Var(X) + Var(Y). Did you expect this result? Why?