Exercise 4.2. 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 S(z, y) = {(x + 2y), 0

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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4.2

 

Exercise 4.2. 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
S{r+ 2y), 0<r<1, 0< y < 1,
10,
f(x, y) =
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:Exercise 4.2. 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 S{r+ 2y), 0<r<1, 0< y < 1, 10, f(x, y) = 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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