{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Hw12 - f x θ = θ x θ – 1 0< x< 1 where θ> 0 a...

This preview shows page 1. Sign up to view the full content.

STAT 410 Homework #12 Spring 2008 (due Thursday, April 17, by 5:00 p.m.) 1. 5.7.4 2. 5.7.5 3. 5.7.6 4. Let X 1 , X 2 , … , X n be a random sample of size n from a N ( 0 , σ 2 ) distribution. a) Find the sufficient statistic Y for σ 2 . ( See 7.2.1 . ) b) Show that the maximum likelihood estimator for σ 2 is a function of Y . c) Is the maximum likelihood estimator for σ 2 unbiased? 5. Let X 1 , X 2 , … , X n be a random sample of size n from a distribution with p.d.f. f ( x ; θ ) = θ
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x ; θ ) = θ x θ – 1 , 0 < x < 1, where θ > 0. a) Find the sufficient statistic Y for θ . b) Show that the maximum likelihood estimator for θ is a function of Y . c) Argue that & ˆ is also sufficient for θ . 6. a) 7.2.4 b) 7.2.7 7. a) 7.2.6 b) 7.2.8 _________________________________________________________________________ If you are registered for 4 credit hours: ( to be handed in separately ) 8. 5.7.9...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern