tut_7_Chap_7_sol - ,QatarUniversity ,GENG200 Tutorial 7 2B...

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College of Engineering, Qatar University Page 1 of 3 Probability and Statistics, GENG200 2B Tutorial - 7 Question Sections 7-3 Page 242: 1) 7.14 SOLUTION: 7-14 E () μ = = = = = = n n X E n n X E X n i i n i i 2 2 1 2 1 2 2 1 2 1 1 E = = = = = = n n X E n n X E X n i i n i i 1 1 1 1 2 , 1 X and 2 X are unbiased estimators of μ . The variances are V 2n 2 1 σ = X and V n 2 2 = X ; compare the MSE (variance in this case), 2 1 2 / 2 / ) ˆ ( ) ˆ ( 2 2 2 1 = = = n n n n MSE MSE Θ Since both estimators are unbiased, examination of the variances would conclude that X 1 is the “better” estimator with the smaller variance. Exercises Sections 7-3 Page 242: 2) 7-15 Answer: 7-15 E [] = = = + + + = ) 7 ( 7 1 )) ( 7 ( 7 1 ) ( ) ( ) ( 7 1 ˆ 7 2 1 1 X E X E X E X E L E = + = + + = ] 2 [ 2 1 ) ( ) ( ) 2 ( 2 1 ˆ 7 6 1 2 X E X E X E a) Both 1 ˆ and 2 ˆ are unbiased estimates of μ since the expected values of these statistics are equivalent to the true mean, μ .
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tut_7_Chap_7_sol - ,QatarUniversity ,GENG200 Tutorial 7 2B...

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