05 - THE UNIVERSITY OF HONG KONG Department of Statistics...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
THE UNIVERSITY OF HONG KONG Department of Statistics And Actuarial Science STAT 1302 PROBABILITY AND STATISTICS II EXAMPLE CLASS 5 1. Let X 1 ,...,X n be independent Poisson random variables with X j having parameter , where λ > 0 is an unknown parameter. (a) Find the Fisher information contained in ( X 1 ,...,X n ) about λ . (b) Find the MLE of λ . What is its i. Bias; ii. Variance; iii. Mean squared error? iv. Is this MLE of λ efficient? 2. Let X 1 ,...,X n be i.i.d. from the uniform distribution over the interval [ θ,θ +1], where θ is unknown. (a) Find a bivariate sufficient statistic for θ . (b) Find a maximum likelihood estimator of θ . (c) Show that max { X 1 ,...,X n } - n 1+ n is an unbiased estimator of θ . 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
3. (a) The likelihood function of λ is l x ( λ ) = p ( x | λ ) = n Y j =1 P ( ) = n Y j =1 ( ) x j exp {- } x j ! = Q n j =1 j x j Q n j =1 x j ! · λ
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/29/2010 for the course STAT 1302 taught by Professor Smslee during the Spring '10 term at HKU.

Page1 / 8

05 - THE UNIVERSITY OF HONG KONG Department of Statistics...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online