tut_7_Chap_7_sol

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

This preview shows pages 1–2. Sign up to view the full content.

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 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online