Stat400Lec14(Ch4.2,5.3)

# Stat400Lec14(Ch4.2,5.3) - STAT 400 Chapter 4.2 5.3 Spring...

This preview shows pages 1–3. Sign up to view the full content.

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: STAT 400 Chapter 4.2, 5.3 Spring 2012 4.2 Covariance and Correlation Coefficient Covariance of X and Y XY = Cov ( X , Y ) = E [ ( X – X ) ( Y – Y ) ] = E ( X Y ) – X Y (a) Cov ( X , X ) = Var ( X ) ; (b) Cov ( X , Y ) = Cov ( Y , X ) ; (c) Cov ( a X + b , Y ) = a Cov ( X , Y ) ; (d) Cov ( X + Y , W ) = Cov ( X , W ) + Cov ( Y , W ) . Cov ( a X + b Y , c X + d Y ) = a c Var ( X ) + ( a d + b c ) Cov ( X , Y ) + b d Var ( Y ) . Var ( a X + b Y ) = Cov ( a X + b Y , a X + b Y ) = a 2 Var ( X ) + 2 a b Cov ( X , Y ) + b 2 Var ( Y ) . 0. Find in terms of X 2 , Y 2 , and XY : a) Cov ( 2 X + 3 Y , X – 2 Y ), b) Var ( 2 X + 3 Y ), c) Var ( X – 2 Y ). Correlation coefficient of X and Y XY = Y X XY σ σ σ = , Y Var X Var Y X Cov = Y Y , X X σ μ σ μ Y X E (a) – 1 XY 1; (b) XY is either + 1 or – 1 if and only if X and Y are linear functions of one another. If random variables X and Y are independent, then E ( g ( X ) h ( Y ) ) = E ( g ( X ) ) E ( h ( Y ) ). Cov ( X, Y ) = XY = 0, Corr ( X , Y ) = XY = 0. 1. Consider the following joint probability distribution p ( x , y ) of two random variables X and Y: y Recall: E ( X ) = 1.75, E ( Y ) = 0.8, E ( X Y ) = 1.5....
View Full Document

## This note was uploaded on 03/14/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

### Page1 / 8

Stat400Lec14(Ch4.2,5.3) - STAT 400 Chapter 4.2 5.3 Spring...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online