This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Problem Set 6 ECON 837 Prof. Simon Woodcock, Spring 2006 Due: March 17 in class 1. Suppose that plim X n = 2 and plim Y n = 3 : Find plim X n Y n ; plim ( X n + Y n ) ; plim ( X 2 n + Y 2 n ) : 2. (Casella and Berger, 1990) Let X 1 ; X 2 ; ::: be a random sequence that converges in probability to a constant a: Assume that Pr [ X i &gt; 0] = 1 for all i: (a) Without using the Slutsky Theorem , show that the random sequence Y 1 ; Y 2 ; ::: de&amp;ned by Y i = p X i converges in probability to p a: (b) Show that if a &gt; ; the sequence Y 1 ; Y 2 ; ::: de&amp;ned by Y i = a=X i converges in probability to 1. 3. Suppose that X n = 3 &amp; 1 n 2 Y n = p n &amp; Z n &amp; where &amp; Z n = 1 n P n i =1 Z i ; and the Z i are iid with mean zero and variance &amp; 2 : Find the limiting distributions of (a) X n + Y n (b) X n Y n (c) Y 2 n : 4. [Final Exam, 2004] Suppose f x i ; y i g n i =1 are an iid random sample from some distribution with at least 4 moments. Denote E [ x ] by x and E [ y ] by y : Let = x &amp; y and let...
View
Full
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.
 Spring '09
 Thewalt
 Physics

Click to edit the document details