A privately owned liquor store operates both a drive-in 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-in and walk-in facilities are in use, and suppose that the joint density function of these variables is

A privately owned liquor store operates both a drive-in 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-in and walk-in facilities are in use, and suppose that the joint density function of these variables is

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Question

2. A privately owned liquor store operates both a drive-in 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-in and walk-in facilities are in use, and suppose that the joint density
function of these variables is
f(x, y) = 5(x + 2y), 0 < x < 1,0 < y s 1,
0,
elsewhere.
a. Find the marginal density of X.
b. Find the marginal density of Y.
c. Find the probability that the drive-in facility is busy less than one-half of the time.

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