A surveyor wishes to lay out a square region with each side hav- ing length L. However,

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A surveyor wishes to lay out a square region with each side hav- ing length L. However, because of a 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

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