A restaurant serves three fixed-price dinners costing $12,

$15, and $20. For a randomly selected couple dining at this restaurant, let X
the cost of the man’s dinner and Y
the cost of the woman’s dinner. The joint pmf of X and Y is given in the following table:

y p(x, y) | 12 15 20 12 | .05 .05 .10 x 15 | .05 .10 .35 20 | 0 .20 .10

a. Compute the marginal pmf’s of X and Y.

b. What is the probability that the man’s and the woman’s dinner cost at most $15 each?

c. Are X and Y independent? Justify your answer.

d. What is the expected total cost of the dinner for the two people?

e. Suppose that when a couple opens fortune cookies at the conclusion of the meal, they find the message “You will receive as a refund the difference between the cost of the more expensive and the less expensive meal that you have chosen.” How much does the restaurant expect to refund?