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. Calculate 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?