{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# fexamA-f09 - Economics 506 FINAL EXAM Version A(Total...

This preview shows pages 1–5. Sign up to view the full content.

Economics 506 FALL 2009 FINAL EXAM Version A (Total Points: 200) Name: ___________________________________e-mail:_______________________ 1) [Total points: 80] Consider the following density function = - - elsewhere 0 0 , 0 1 ) ( 1 y e ry y f r y r θ θ θ where r is a known positive constant. a) [10 points] use the method of transformation to find the density function of U = Y r b) [10 points] Let Y 1 , Y 2 , …, Y n denote a random sample from the density function given above. Find a sufficient statistics for θ. (Use the back side if you need to) 1

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

View Full Document
Economics 506 FALL 2009 FINAL EXAM c) [10 points] Use method of moment generating function to find the distribution of the sufficient statistics you found in part (b). d) [10 points] Let Y 1 , Y 2 , …, Y n denote a random sample from the density function given above. Find the maximum likelihood estimator (MLE) of θ (Use the back side if you need to) 2
Economics 506 FALL 2009 FINAL EXAM e) [5 points] Is the MLE you found in part (d) a MVUE (minimum variance unbiased estimator) for θ? f) [10 points] find the minimum variance of an unbiased estimator of θ , using Rao- Cramer inequality. Confirm that it is the same as the variance of the MLE you found in part (d). (Use the back side if you need to) 3

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

View Full Document
Economics 506 FALL 2009 FINAL EXAM g) [15 points] s uppose r = 1 . Assume we take a sample of size 40 observations and find out that = = 40 1 160 i i y . Use the Neyman-Pearson lemma to find the most powerful test of
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

fexamA-f09 - Economics 506 FINAL EXAM Version A(Total...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online