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

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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 ∞∞ −∞ = = ∫∫
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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 ∞∞ −∞ −∞ = = ∑∑ ∫∫
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4.2 Variance and Covariance Let X
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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.

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

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