A privately owned iquor store operates both a drive-in facility and a walik-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 facilites are in use, and suppose that the joint density function of these variables is (x.y) = Ea + 2y),0SIS 10sysi. 0. elsewhere. a. Find the marginal density of X. b. Find the marginal density of Y. C. Find the probability that the drive-in facilty is busy less than one-halt of the time.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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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 facilites are in use, and suppose that the joint density
function of these variables is
(r. y) =x + 2y),0 SrS 1,0 sys1,
0,
(x.y)
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.
Transcribed Image Text: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 facilites are in use, and suppose that the joint density function of these variables is (r. y) =x + 2y),0 SrS 1,0 sys1, 0, (x.y) 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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