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# Lecturenotes8 - STAT 430/510 Lecture 8 STAT 430/510...

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STAT 430/510 Lecture 8 STAT 430/510 Probability Hui Nie Lecture 8 June 8th, 2009

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STAT 430/510 Lecture 8 Review Properties of Probability Deﬁnition of Random Variable pmf and cdf of Discrete Random Variables Expected Value
STAT 430/510 Lecture 8 Introduction Expected value yields the weighted average of the possible values of the random variable. Variance gives us the information on the variation or spread of these values.

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STAT 430/510 Lecture 8 Deﬁnition If X is a random variable with mean μ , then the variance of X , denoted by Var ( X ) , is deﬁned by Var ( X ) = E [( X - μ ) 2 ] An alternative formula for Var ( X ) is Var ( X ) = E [ X 2 ] - ( E [ X ]) 2 The square root of the Var ( X ) is called the standard deviation of X . Denote it by SD ( X ) , that is, SD ( X ) = p Var ( X )
STAT 430/510 Lecture 8 Example Calculate Var ( X ) if X represents the outcome when a fair die is rolled. Var ( X ) = 35 12 . Why?

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STAT 430/510 Lecture 8 Property of Variance For any constant a and b , Var ( aX + b ) = a 2 Var ( X ) For any constant a and b , SD ( aX + b ) = aSD ( X )
Example Assume that Var ( X ) = 1. Calculate Var ( 7 X + 2 ) . Solution:

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Lecturenotes8 - STAT 430/510 Lecture 8 STAT 430/510...

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