A surveyor wishes to lay out a square region with each side having length L. However, because

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A surveyor wishes to lay out a square region with each side having length L. However, because of measurement error, he instead lays out a rectangle in which the north–south sides both have length X and the east–west sides both have length Y. Suppose that X and Y are independent and that each is uniformly distributed on the interval [L A, L A]

(where 0 A L). What is the expected area of the resulting rectangle?

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