Question: 19. Let X be a random variable with probability density function fe(r), which depends on the parameter 0. Assume that all regularity conditions for commuting

19. Let X be a random variable with probability density function fe(r), which depends on the parameter 0. Assume that all regularity conditions for commuting the order of differentiation and integration are satisfied. (a) Show that E ae log fe(X) = 0 (b) Let e be an unbiased estimator for 0. Use the result in (a) in conjunction with the Cauchy-Schwarz inequality to prove that V (0) 2 E Blog fo(X)

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