Lecture18_Chapter4

# Lecture18_Chapter4 - Lecture 18 Chapter 4 Monday, October...

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Lecture 18 – Chapter 4 Monday, October 27 th

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Expected value ± The expected value of a continuous random variable X with pdf f(x) is () ( ) x E Xx f xd x μ −∞ ==
Example 4.10 page 168

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Properties of expected value ± If X is a continuous random variable with pdf f(x) and h(x) is any function of X, then ± In example 4.10 of the book find E(X 2 ). () hX E hx f x d x μ −∞ ==
Variance ± The variance of a continuous random variable X with pdf f(x) and mean value is: ± The standard deviation (SD) of X is μ () ( ) ( ) 22 2 X VX E X x fx d x σμ −∞ ==− = X σ =

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Properties ± The same properties as in the discrete case applies () ( ) 2 2 VX E X E X =− ( ) ( ) Ea X b a E X b + =+ ( ) ( ) 2 Va X b a V X += ( ) ( ) SD aX b a SD X
Example ± Find the variance and standard deviation in Example 4.10 of the book.

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## This note was uploaded on 09/23/2009 for the course STAT 318 taught by Professor Staff during the Fall '08 term at Penn State.

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Lecture18_Chapter4 - Lecture 18 Chapter 4 Monday, October...

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