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? $
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning