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Unformatted text preview: F : f ( x ) = d dx F ( x ) = nx n1 n , < x < . So the expected value of is E ( ) = Z x nx n1 n dx = n ( n + 1) n x n +1 = n n + 1 . 1 OR 2700, Spring 09 Section 10 We see that E ( ) 6 = , which means that is a biased estimator for . Note that E n + 1 n = n + 1 n E ( ) = n + 1 n n n + 1 = , so n +1 n max { X 1 ,...,X n } is an unbiased estimator for . d. We compute E ( 2 ) = Z x 2 nx n1 n dx = n ( n + 2) n x n +2 = n n + 2 2 . Therefore, Var( ) = n n + 2 2 n n + 1 2 = n n + 2n 2 ( n + 1) 2 2 and SE = s n n + 2n 2 ( n + 1) 2 . In order to estimate the standard error from the data, we may replace with . 2...
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This note was uploaded on 09/06/2009 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell University (Engineering School).
 Spring '05
 STAFF

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