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.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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2. A fast-food restaurant operates both a drive-through facility and walk-in facility. On a randomly
selected day, let X and Y, respectively, be the proportion of the time that the drive-thorugh and walk-
in facilities are in use, and suppose that the joint density function of these random variables is
f(x,y) = }3
(x + 2y), 0<x < 1, 0Sys1,
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.
Transcribed Image Text:2. A fast-food restaurant operates both a drive-through facility and walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportion of the time that the drive-thorugh and walk- in facilities are in use, and suppose that the joint density function of these random variables is f(x,y) = }3 (x + 2y), 0<x < 1, 0Sys1, 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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