Chapter 4

# Chapter 4 - Chapter 4. Mathematical Expectation 4.1 Mean of...

This preview shows pages 1–4. Sign up to view the full content.

Chapter 4. Mathematical Expectation 4.1 Mean of a Random Variable Let X be a random variable with probability distribution f ( x ). The mean or expected value of X is ( ) . . () () .. all x xf x if X is discrete r v EX xf x dx if X is continuous r v µ −∞ == Let X be a random variable with probability distribution f ( x ). The mean or expected value of the random variable g ( x ) is ( ) ( ) . . [() ] () () all x gx g x f x if X is discrete r v Egx g x f x dx if X is continuous r v −∞ Ex 4.3) X = the life in hours a certain electronic device. 3 20000 , 100 0 , elsewhere x fx x > = 3 100 20000 ( ) ( ) 200 x f xd x x d x x ∞∞ −∞ = = ∫∫

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

View Full Document
Le t X and Y be a random variable with joint probability distribution f ( x, y ). The mean or expected value of the random variable g ( X, Y ) is (,) [( ,) ] ( , ) ( , ) . . (, ) (, ) .. gXY all x all y EgXY g x y f x y if X and Y is discrete r v g x y f x y dxdy if X and Y is continuous r v µ ∞∞ −∞ −∞ = = ∑∑ ∫∫
4.2 Variance and Covariance Let X

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.

## This note was uploaded on 10/02/2011 for the course STAT 3011 taught by Professor Wang,zhan during the Spring '09 term at Minnesota.

### Page1 / 5

Chapter 4 - Chapter 4. Mathematical Expectation 4.1 Mean of...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online