02_11 - 1 + X 2 . ( ) ( ) 2 1 2 1 2 1 1 1 2 2 1 x m x m e m...

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

View Full Document Right Arrow Icon
STAT 410 Examples for 02/11/2008 Spring 2008 1. Let X and Y be two independent Exponential random variables with mean 1. Find the probability distribution of Z = X + Y. That is, find ( ) z f Z = ( ) z f Y X + . 2. Let X and Y be two independent Exponential random variables with mean 1. Find the p.d.f. of Z = 2 X + Y. Fact : Let X and Y be independent continuous random variables. Then ( ) ( ) ( ) - = - + dx x w f x f w f Y X Y X . (convolution) 3. Let X 1 and X 2 be be two independent χ 2 random variables with m and n degrees of freedom, respectively. Find the probability distribution of W = X
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 + X 2 . ( ) ( ) 2 1 2 1 2 1 1 1 2 2 1 x m x m e m x f--Γ = , x 1 > 0, ( ) ( ) 2 1 2 2 2 2 2 2 2 2 1 x n x n e n x f--Γ = , x 2 > 0. 4. Let X and Y be i.i.d. Uniform [ , 1 ] random variables Find the probability distribution of W = X + Y. That is, find ( ) w f Y X + . 5. Let X and Y be two independent Poisson random variables with mean λ 1 and λ 2 , respectively. Let W = X + Y. a) What is the probability distribution of W? b) What is the conditional distribution of X given W = n ?...
View Full Document

This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.

Ask a homework question - tutors are online