Question

10. Let and consider approximating its average value on the interval (0,2) given by the integral 4-2 dx. 0 (a) Use Calculus to show that the the exact answer is π/2. (Hint: You may want to substitute 2 sin , and later use the trignometric identify cos(20)-1-2 cos2 θ). (b) Assume r is uniformly distributed in (0,2). What is the expected value, E f ()] How is the formula for expected value related to the expression given by expression in (1)? (c) Again assume that is uniformly distributed in (0,2) Show (by using calculus) that the variance, ơ2[f(z), is (8/3_ /4).

Answer 1

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