Question

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. p(x, y) y 12 15 20 x 12 0.05 0.35 0.10 15 0.00 0.20 0.10 20 0.05 0.05 0.10 a) Compute the marginal pmf of X. x 12 15 20 pX(x) b) Compute the marginal pmf of Y. y 12 15 20 pY(y) c) What is the probability that the man's and the woman's dinner cost at most $15 each? d) Are X and Y independent? Justify your answer. e) What is the expected total cost, in dollars, of the dinner for the two people? f) 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 would the restaurant expect to refund, in dollars?

          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.

p(x, y)
   y
12  15  20
x
12  0.05  0.35  0.10
15  0.00  0.20  0.10
20  0.05  0.05  0.10

a) Compute the marginal pmf of X.
   x
12  15  20
pX(x)

b) Compute the marginal pmf of Y.
   y
12  15  20
pY(y)

c) What is the probability that the man's and the woman's dinner cost at most $15 each?

d) Are X and Y independent? Justify your answer.

e) What is the expected total cost, in dollars, of the dinner for the two people?

f) 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 would the restaurant expect to refund, in dollars?

Added by Jaime H.

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