Determine what is wrong with the following argument:
Chapter 8, Problem 13(choose chapter or problem)
Determine what is wrong with the following argument: Suppose that the random variableX has the uniform distribution on the interval [0, ], where the value of is unknown ( > 0). Then f (x| ) = 1/, (x| ) = log and (x| ) = (1/ ). Therefore, I ( ) = E {[ (X| )] 2} = 1 2 . Since 2X is an unbiased estimator of , the information inequality states that Var(2X) 1 I ( ) = 2. But Var(2X) = 4 Var(X) = 4 . 2 12 = 2 3 < 2. Hence, the information inequality is not correct
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