# ps2 - Problem Set 2 ECON 837 Prof. Simon Woodcock, Spring...

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

Problem Set 2 ECON 837 Prof. Simon Woodcock, Spring 2006 Due: Friday Feb 3 (Some problems are based on questions in Casella and Berger Statistical Inference , 1990). 1. Let X 1 and X 2 be independent N (0 ; 1) random variables. Find the pdf of ( X 1 X 2 ) 2 = 2 : 2. Let ( X; Y ) be a bivariate random vector with joint pdf f ( x; y ) : Let U = aX + b and V = cY + d; where a; b; c; and d a > 0 and c > 0 : Show that the joint pdf of ( U; V ) is f U;V ( u; v ) = 1 ac f u b a ; v d c ± : 3. Let X ± N ( ± 2 ) and let Y ± N ( ²; ± 2 ) : Suppose X and Y U = X + Y and V = X Y: Show that U and V are independent normal random f U ( u ) and f V ( v ) : 4. Prove Theorem 10 from Lecture 3 (sampling distribution of x and s 2 under normality). 5. One observation X is taken from a N (0 ; ± 2 ) population. Find an unbiased estimator of ± 2 : Is j X j a su¢ cient statistic? 6. ["Warmup" question from 2004 Midterm] Let

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/08/2011 for the course PHYS 102 taught by Professor Thewalt during the Spring '09 term at Simon Fraser.

### Page1 / 2

ps2 - Problem Set 2 ECON 837 Prof. Simon Woodcock, Spring...

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

View Full Document
Ask a homework question - tutors are online