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 {(2²+y² ), 0

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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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
{(2²+y² ), 0 <x, y < 1
f(x, y) =
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 {(2²+y² ), 0 <x, y < 1 f(x, y) = 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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