Chap4 MTH3401 part3

Chap4 MTH3401 part3 - Chap 4 Mathematical Expectation 1...

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Unformatted text preview: Chap 4 Mathematical Expectation 1 Chapter 4 Mathematical Expectation Chap 4 Mathematical Expectation 2 Means and Variance of Linear Combinations of Random Variables Theorem 4.10: If X and Y are random variables with joint probability distribution f ( x , y ), then Proof . 2 2 2 2 2 2 XY Y X bY aX ab b a + + = + XY Y X Y X Y X Y X Y X bY aX Y X bY aX bY aX bY aX ab b a Y X abE Y E b X E a Y b X a E b a bY aX E b a Y bE X aE bY aX E bY aX E 2 )] )( [( 2 ] ) [( ] ) [( } )] ( ) ( {[ } )] ( ) {[( ) ( ) ( ) ( } ] ) {[( 2 2 2 2 2 2 2 2 2 2 2 2 2 + + =-- +- +- =- +- = +- + = + = + = + =- + = + + + + Chap 4 Mathematical Expectation 3 Means and Variance of Linear Combinations of Random Variables Corollary 1: If X and Y are independent random variables, then Corollary 2: If X and Y are independent random variables, then Corollary 3: If X 1 , X 2 , , X n are independent random variables, then ....
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This note was uploaded on 03/04/2011 for the course MAT 3401 taught by Professor Munther during the Spring '11 term at Cal Poly Pomona.

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Chap4 MTH3401 part3 - Chap 4 Mathematical Expectation 1...

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