h7 - Stat 5101 (Geyer) Fall 2011 Homework Assignment 7 Due...

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

View Full Document Right Arrow Icon
Stat 5101 (Geyer) Fall 2011 Homework Assignment 7 Due Wednesday, November 2, 2011 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. 7-1. If X has the Gam( α,λ ) distribution, we calculated in class that E ( X β ) = Γ( α + β ) Γ( α ) λ β . (a) Find E ( X 2 ) (b) Find var( X ). None of your answers should contain gamma functions (use the gamma function recursion formula to simplify). 7-2. If X has the Beta( α 1 2 ) distribution, show that E { X β 1 (1 - X ) β 2 } = Γ( α 1 + α 2 )Γ( α 1 + β 1 )Γ( α 2 + β 2 ) Γ( α 1 )Γ( α 2 )Γ( α 1 + α 2 + β 1 + β 2 ) Hint: use the fact that the PDF of the beta distribution integrates to one, just like we did for the gamma distribution. You may ignore the issue of when the integral exists (it exists when β 1 > - α 1 and β 2 > - α 2 , but we don’t know how to prove that yet). 7-3. Suppose X has the Beta( α 1 2 ) distribution. (a) Find
Background image of page 1

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

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

Page1 / 4

h7 - Stat 5101 (Geyer) Fall 2011 Homework Assignment 7 Due...

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

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