MA519_JAN03 - QUALIFYING EXAMINATION JANUARY 2003 MATH 519...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
QUALIFYING EXAMINATION JANUARY 2003 MATH 519 - Prof. Sellke Grading: Ten points for each problem 1. Find the greatest possible value of E ( XY ), if X is Exponential ( λ =1 )and Y is discrete uniform on { 1 , 2 } . Justify your answer. 2. Let X 1 ,X 2 ,... be iid Exponential ( λ = 1) random variables. Let M n =max { X 1 ,...,X n } . Find constants c n so that the difference D n = M n - c n converges in distribution, and find the limiting distribution. 3. Let X 1 ,X 2 ,... be iid Exponential ( λ = 1) random variables, and let L n = min { X 1 ,...,X n } . Show that the quotient L 2 n L n converges in distribution, and find the c.d.f. of the limiting distribution. 4. Let ( X,Y ) be a random point in R 2 , distributed uniformly on the interior of the unit circle. Find the density of T = X + Y . 5. Each day, starting on January 1, 2002, Professor Sellke has recorded the value of a standard normal random variable, generated according to the precepts of Professor
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 01/25/2012.

Ask a homework question - tutors are online