Assignment 12

Assignment 12 - Stat 5101 (Geyer) Fall 2009 Homework...

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

View Full Document Right Arrow Icon
Stat 5101 (Geyer) Fall 2009 Homework Assignment 12 Due Wednesday, December 16, 2009 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. 12-1. Give the details of the argument that the Poi( μ ) distribution is ap- proximately normal when μ is large. 12-2. Suppose X 1 , X 2 , ... are IID with mean μ and variance σ 2 and X n = 1 n n X i =1 X i What is the approximate normal distribution of sin( X n ) when n is large? 12-3. Suppose X 1 , X 2 , ... are IID Poi( μ ) random variables and X n = 1 n n X i =1 X i To what random variable does n ( e - X n - e - μ ) converge in distribution? 12-4. Suppose X 1 , X 2 , ... are IID Ber( p ) random variables with 0 < p < 1 and X n = 1 n n X i =1 X i (a) What is the approximate normal distribution of X n (1 - X n ) when n is large? (b) There is something unusual about the case
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 / 2

Assignment 12 - Stat 5101 (Geyer) Fall 2009 Homework...

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