SOLUTION: A surveyor wishes to lay out a square region with each side having length 10 Units. However, because of a measurement error, he instead lays out a rectangle in which the north -

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Question 1178033: A surveyor wishes to lay out a square region with each side having length 10 Units. 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 [8, 12]. What is the expected area of the resulting rectangle?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The prob'y density function of X (or Y) is f%28x%29+=+1%2F4, being distributed uniformly.
==> E%28X%29+=+%281%2F4%29%2A%28int%28x%2Cdx%2C8%2C12%29+%29=+10. Similarly, E%28Y%29+=+10, Y being identical distributionally to X.
==> E%28A%29+=+E%28XY%29+=+E%28X%29%2AE%28Y%29+=+10%2A10+=+100, since X and Y are independent random variables.