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A restaurant serves three fixed-price dinners costing $11, $14, and $19. 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. X Px(x) p(x, y) 11 14 19 (a) Compute the marginal pmf of X. y X Py(y) 11 y 14 19 0.10 0.35 0.10 0.10 11 0.05 0.00 0.20 0.05 0.05 Compute the marginal pmf of Y. 11 14 14 19 19 (b) What is the probability that the man's and the woman's dinner cost at most $14 each? (c) Are X and Y independent? Justify your answer. O X and Y are not independent because P(x, y) = Px(x) Py(Y). X and Y are not independent because P(x, y) # P(x) Py(Y). O X and Y are independent because P(x, y) = Px(x) Py(Y). O X and Y are independent because P(x, y) # Px(x) Py(y). . . (d) What is the expected total cost, in dollars, 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 would the restaurant expect to refund, in dollars? $

A restaurant serves three fixed-price dinners costing $11, $14, and $19. 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. X Px(x) p(x, y) 11 14 19 (a) Compute the marginal pmf of X. y X Py(y) 11 y 14 19 0.10 0.35 0.10 0.10 11 0.05 0.00 0.20 0.05 0.05 Compute the marginal pmf of Y. 11 14 14 19 19 (b) What is the probability that the man's and the woman's dinner cost at most $14 each? (c) Are X and Y independent? Justify your answer. O X and Y are not independent because P(x, y) = Px(x) Py(Y). X and Y are not independent because P(x, y) # P(x) Py(Y). O X and Y are independent because P(x, y) = Px(x) Py(Y). O X and Y are independent because P(x, y) # Px(x) Py(y). . . (d) What is the expected total cost, in dollars, 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 would the restaurant expect to refund, in dollars? $

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A restaurant serves three fixed-price dinners costing $11, $14, and $19. 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. X Px(x) p(x, y) 11 14 19 X (a) Compute the marginal pmf of X. y Py(y) 11 y 14 19 0.10 0.35 0.10 0.10 11 0.05 0.00 0.20 0.05 0.05 11 Compute the marginal pmf of Y. 14 14 19 19 (b) What is the probability that the man's and the woman's dinner cost at most $14 each? (c) Are X and Y independent? Justify your answer. O X and Y are not independent because P(x, y) = Px(x) Py(Y). X and Y are not independent because P(x, y) # Px(x) Py(Y). O X and Y are independent because P(x, y) = Px(x) · Py(Y). O X and Y are independent because P(x, y) # Px(x) · Py(Y). . (d) What is the expected total cost, in dollars, 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 would the restaurant expect to refund, in dollars? $
Transcribed Image Text:A restaurant serves three fixed-price dinners costing $11, $14, and $19. 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. X Px(x) p(x, y) 11 14 19 X (a) Compute the marginal pmf of X. y Py(y) 11 y 14 19 0.10 0.35 0.10 0.10 11 0.05 0.00 0.20 0.05 0.05 11 Compute the marginal pmf of Y. 14 14 19 19 (b) What is the probability that the man's and the woman's dinner cost at most $14 each? (c) Are X and Y independent? Justify your answer. O X and Y are not independent because P(x, y) = Px(x) Py(Y). X and Y are not independent because P(x, y) # Px(x) Py(Y). O X and Y are independent because P(x, y) = Px(x) · Py(Y). O X and Y are independent because P(x, y) # Px(x) · Py(Y). . (d) What is the expected total cost, in dollars, 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 would the restaurant expect to refund, in dollars? $
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