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1. A bank operates a drive-up and walk-up window. Let X = the proportion of the time the drive-up facility is in use and let Y = the proportion of the time the walk-up window is in use. Suppose the operations manager uses the following distribution as the joint pdf based on his historical data: f(x, y) = 5 = { 2(x + y²) if 0 (x + y²) if 0 ≤ x ≤ 1 and 0 ≤ y ≤1 otherwise (a) Find the marginal pdf for X, fx(x). (b) Find the marginal pdf for Y, fy(y).

1. A bank operates a drive-up and walk-up window. Let X = the proportion of the time the drive-up facility is in use and let Y = the proportion of the time the walk-up window is in use. Suppose the operations manager uses the following distribution as the joint pdf based on his historical data: f(x, y) = 5 = { 2(x + y²) if 0 (x + y²) if 0 ≤ x ≤ 1 and 0 ≤ y ≤1 otherwise (a) Find the marginal pdf for X, fx(x). (b) Find the marginal pdf for Y, fy(y).

Calculus For The Life Sciences
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.
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1. A bank operates a drive-up and walk-up window. Let X = the proportion of the time the drive-up facility is in use and let Y = the proportion of the time the walk-up window is in use. Suppose the operations manager uses the following distribution as the joint pdf based on his historical data: f(x, y) = 5 - 1/2(x + y²) if 0 (x + y²) if 0 ≤ x ≤ 1 and 0 ≤ y ≤1 otherwise (a) Find the marginal pdf for X, fx(x). (b) Find the marginal pdf for Y, fy(y).
Transcribed Image Text:1. A bank operates a drive-up and walk-up window. Let X = the proportion of the time the drive-up facility is in use and let Y = the proportion of the time the walk-up window is in use. Suppose the operations manager uses the following distribution as the joint pdf based on his historical data: f(x, y) = 5 - 1/2(x + y²) if 0 (x + y²) if 0 ≤ x ≤ 1 and 0 ≤ y ≤1 otherwise (a) Find the marginal pdf for X, fx(x). (b) Find the marginal pdf for Y, fy(y).
(c) Are the random variables X and Y independent? Show work to support your answer.
Transcribed Image Text:(c) Are the random variables X and Y independent? Show work to support your answer.
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