Lecture 13-2007

# Lecture 13-2007 - Bivariate and Multivariate Normal Random...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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.

Unformatted text preview: Bivariate and Multivariate Normal Random Variables Lecture XIII Bivariate Normal Random Variables Definition 5.3.1. The bivariate normal density is defined by ( 29 ( 29 - -- - + ---- = Y Y X X Y Y X X Y X y x y x y x f 2 1 2 1 exp 1 2 1 , 2 2 2 2 Theorem 5.3.1. Let ( X , Y ) have the bivariate normal density. Then the marginal densities f ( x ) and f ( y ) and the conditional densities f ( y | x ) and f ( x | y ) are univariate normal densities, and we have E [ X ]= X , V [ X ]= X 2 , E [ Y ]= Y , V [ Y ]= Y 2 , Corr ( X , Y )= , and [ ] ( 29 [ ] ( 29 2 2 | | 1 Y Y X X Y E Y X X V Y X = + - = - ( 29 ( 29 ( 29 ( 29 1 2 2 2 2 2 2 2 2 1 exp 2 1 1 2 1 exp 1 2 1 , f f x x y y x f X X X X X Y Y Y Y = -- ------ = where f 1 is the density of N ( X , X 2 ) and f 2 is the density function of...
View Full Document

## This note was uploaded on 11/08/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

### Page1 / 17

Lecture 13-2007 - Bivariate and Multivariate Normal Random...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online