a. Compute the probability that neither line is busy more than half the time. b. Find the probability that the first line is busy more than 75% of the time.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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Two service lines are operated in a service facility. On a randomly selected
day, let X be the proportion of the time that the first line is in use whereas Y is the
proportion of time that the second line is in use. Suppose that the joint probability
density function for (X, Y) is
f(x, y) = { 7(x* + y²), 0<x,y< 1
elsewhere
a. Compute the probability that neither line is busy more than half the time.
b. Find the probability that the first line is busy more than 75% of the time.
Transcribed Image Text:Two service lines are operated in a service facility. On a randomly selected day, let X be the proportion of the time that the first line is in use whereas Y is the proportion of time that the second line is in use. Suppose that the joint probability density function for (X, Y) is f(x, y) = { 7(x* + y²), 0<x,y< 1 elsewhere a. Compute the probability that neither line is busy more than half the time. b. Find the probability that the first line is busy more than 75% of the time.
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