Question: If X be a random variable with mean and variance 2 and suppose that h(x) is differentiable function with h'() 6 not equal to 0,
If X be a random variable with mean and variance 2 and suppose that h(x) is differentiable function with h'() 6 not equal to 0, then the expectation and variance of Y = h(X) can be approximated as E(h(X)) h() and V(h(X)) (h'())2V(X). This is known as the delta method and the justification for the approximations follows from a first-order Taylor series expansion Y = h(X) h() + h'()(X ). Now let X Uniform(0, 1), then the variance of Y = 1 /X by delta method is approximately
(A) 1/2
(B) 1/3
(C) 2/3
(D) 3/4
(E) None of the above.
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