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Unformatted text preview: Homework 8 1. a. implies that 2 ) ( 2 = X E = 2 2 X E . Consider n X i 2 2 = . Then ( ) ( ) = = = = = n n n n X E n X E E i i 2 2 2 2 2 2 2 2 , implying that is an unbiased estimator for . b. , so 1058 . 1490 2 = i x 505 . 74 20 1058 . 1490 = = 3. a. We wish to take the derivative of , set it equal to zero and solve for p. ( ) x n x p p x n 1 ln ( ) ( ) ( ) p x n p x p x n p x x n dp d = + + 1 1 ln ln ln ; setting this equal to zero and solving for p yields n x p = . For n = 20 and x = 3, 15 . 20 3 = = p b. ( ) ( ) ( ) p np n X E n n X E p E = = = = 1 1 ; thus is an unbiased estimator of p. p c. ( ) 4437 . 15 . 1 5 = 4....
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 Spring '05
 STAFF

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