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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
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Solved: A fast-food restaurant operates both a

Chapter 4, Problem 3.40

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QUESTION:

A fast-food restaurant operates both a drivethrough facility and a walk-in facility. On a randomly selected day, let X and Y , respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is f(x,y)=2 3(x +2y), 0 x 1, 0 y 1, 0, elsewhere. (a) Find the marginal density of X. (b) Find the marginal density of Y . (c) Find the probability that the drive-through facility is busy less than one-half of the time.

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QUESTION:

A fast-food restaurant operates both a drivethrough facility and a walk-in facility. On a randomly selected day, let X and Y , respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is f(x,y)=2 3(x +2y), 0 x 1, 0 y 1, 0, elsewhere. (a) Find the marginal density of X. (b) Find the marginal density of Y . (c) Find the probability that the drive-through facility is busy less than one-half of the time.

ANSWER:

A fast-food restaurant operates both a drive through facility and a walk-in facility. On arandomly selected day, let X and Y , respectively, be the proportions of the time that thedrive-through and walk-in facilities are in use, and suppose that the joint density functionof these random variables is(a) Find the marginal density of X.(b) Find the marginal density of Y .(c) Find the probability that the drive-through facility is busy less than one-half of the time. Step By Step SolutionStep 1 of 3:(a) Find the marginal density of X.The joint probability function of x and y proportions is given by:Marginal density of X is given as:Thus marginal density of X is

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