Use the result of Exercise 28 to show that when X and Y are independent, Cov(X, Y) = Cor...

Use the result of Exercise 28 to show that when X and Y are independent, Cov(X, Y) = Corr(X, Y) = 0.

Reference exercise 28

Show that if X and Y are independent rv’s, then E(XY) = E(X) . E(Y). Then apply this in Exercise 25. [Hint: Consider the continuous case with f(x, y) = fX(x) . fY (y).]

Reference exercise 25

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–A, L+A] (where 0<A). What is the expected area of the resulting rectangle?