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Unformatted text preview: IE121 HW#2 Solutions 72. E ( 29 [ ] = = = + + + = ) 7 ( 7 1 )) ( 7 ( 7 1 ) ( ) ( ) ( 7 1 7 2 1 1 X E X E X E X E E ( 29 [ ] = + = + + = ] 2 [ 2 1 ) ( ) ( ) 2 ( 2 1 7 6 1 2 X E X E X E a) Both 1 and 2 are unbiased estimates of since the expected values of these statistics are equivalent to the true mean, . b) V ( 29 ( 29 2 2 7 2 1 2 7 2 1 1 7 1 ) 7 ( 49 1 ) ( ) ( ) ( 7 1 7 ... = = + + + = + + + = X V X V X V X X X V 7 ) ( 2 1 = V V ( 29 ( 29 )) ( ) ( ) ( 4 ( 4 1 ) ( ) ( ) 2 ( 2 1 2 2 4 6 1 4 6 1 2 4 6 1 2 X V X V X V X V X V X V X X X V + + = + + = + = = ( 29 1 4 4 2 2 2 + + = 1 4 6 2 ( ) 2 3 ) ( 2 2 = V Since both estimators are unbiased, the variances can be compared to decide which is the better estimator. The variance of 1 is smaller than that of 2 , 1 is the better estimator....
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This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .
 Spring '08
 Perevalov

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