*3.9.9.** *Find *E**(** **R**)** *for a two-resistor circuit similar to the one dbed in Example 3.9.2. where *fx.y**(** x , *y) = *k**(** **x** *+ y). 10 *::S** **x** **::S** *20, 10 *::S** **y** ::S *20.

3.9.10. Suppose that *X *and *Y *are both uniformly distributed over the interval [O, 1J. Calculate

the expected value of the square of the distance of the random point *( X , Y) *from the origin; that is, find £(X2 + Y 2). *Hinr: *See Question 3.85.

3.9.11. Suppose *X *represen ts a poin t picked at random from the interval [O, 1] on the x-axis, and *Y *is a point picked at random from the interval [0. 1] on the *y-a xis. *Assume that. *X *and *Y *are independent. Wha t is the expected value of the area of the triangle formed by the points (X, 0), (0. Y) and (0,0)? ·

3.9.12. Suppose *Y**1 **, **Yi• .... Y,, **is *a random sample from the unifonn pdf over [O, 1]. The geometric mean of the numbers is the random variable ,v'Y1*Yi** *· ··· · *Y,,.** *Compare the expected value of the geometric mean to that of the arithmetic mean *Y.*

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