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 Y1 , Yi• .... Y,, is a random sample from the unifonn pdf over [O, 1]. The geometric mean of the numbers is the random variable ,v'Y1Yi · ··· · Y,,. Compare the expected value of the geometric mean to that of the arithmetic mean Y.
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