Question: A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is

A service facility operates with two service lines. On a randomly selected day, let X be the proportion of 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 1. Compute the probability that neither line is busy more than half the time.

2. Find the probability that the first line is busy more than 75%

of the time.

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