{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

h8 - Stat 5102(Geyer Spring 2012 Homework Assignment 8 Due...

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

View Full Document Right Arrow Icon
Stat 5102 (Geyer) Spring 2012 Homework Assignment 8 Due Wednesday, March 28, 2012 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 8-1. Show that each of the following is an exponential family. Identify the natural parameter and natural statistic. (a) The Poi( μ ) family of distributions. (b) The Exp( λ ) family of distributions. (c) The Gam( α,λ ) family of distributions with both parameters unknown. The natural parameter vector and natural statistic vector are both two- dimensional. 8-2. Suppose X is Poi( μ ) and the prior distribution for μ is Gam( α,λ ), where α and λ are hyperparameters. Find the posterior distribution for μ . 8-3. Suppose X 1 , ... , X n are IID Gam( α,λ ), where α is known and λ is unknown. Suppose the prior distribution for λ is Gam( α 0 0 ), where α 0 and λ 0 are hyperparameters. Find the posterior distribution for
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

h8 - Stat 5102(Geyer Spring 2012 Homework Assignment 8 Due...

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

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