2. A fast-food restaurant operates both a drive through 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) =(x + 2y), 0

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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2. A fast-food restaurant operates both a drive through 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) = (x+ 2y), 0<x< 1,0 <y<1
(a) Find the marginal probability density function of X.
(b) Find the marginal probability density function of Y.
(c) Find the conditional probability density function of X.
(d) Find the conditional probability density function of Y.
(e) Are X and Y independent? (You need to explain.)
(f) 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 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) = (x+ 2y), 0<x< 1,0 <y<1 (a) Find the marginal probability density function of X. (b) Find the marginal probability density function of Y. (c) Find the conditional probability density function of X. (d) Find the conditional probability density function of Y. (e) Are X and Y independent? (You need to explain.) (f) Find the probability that the drive-through facility is busy less than one-half of the time.
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