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

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

View Full Document Right Arrow Icon
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
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.

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 Right Arrow Icon
Ask a homework question - tutors are online