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 f(x, y) = 3 2 (x2 + y2), 0 ≤ x, y ≤ 1, 0, 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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