A surveyor wishes to lay out a square region with each sidehaving 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 lengthY. Suppose that X and Y are independent and that each isuniformly distributed on the interval [L 2 A, L 1 A] (where0 , A , L). What is the expected area of the resultingrectangle?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A surveyor wishes to lay out a square region with each side
having 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 2 A, L 1 A] (where
0 , A , L). What is the expected area of the resulting
rectangle?

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