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A bank operates a drive-up facility and a walk-up window. On a randomly selected day, let...

A bank operates a drive-up facility and a walk-up window. On a randomly selected day, let X be the proportion of time the drive-up facility is in use, and Y be the proportion of time the walk-up window is in use. The joint support is Ω = {0 ≤ X ≤ 1, 0 ≤ Y ≤ 1}, and the joint pdf is given by

f (x, y) = (6/5)*(x + y^(2) ) where (x, y) ∈ Ω

Find the probability that neither facility is busy more than 1/4 of the time.

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