Slides05-2010

Slides05-2010 - Outline Expected Value Moments of a Distribution Expected Value and Moments Charles B Moss Charles B Moss Expected Value and

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Outline Expected Value Moments of a Distribution Expected Value and Moments Charles B. Moss August 28, 2010 Charles B. Moss Expected Value and Moments

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Outline Expected Value Moments of a Distribution Expected Value Empirical Moments Applications Bivariate Random Variables Moments of a Distribution Moments of the Uniform Distribution Charles B. Moss Expected Value and Moments
Outline Expected Value Moments of a Distribution Empirical Moments Applications Bivariate Random Variables Expected Value I The random variable can also be described using a statistic. I One basic statistic encountered by students in statistics courses is the mean of a random variable. I DeFnition 2.12 p-28 The expected value (expectation or mean) of a discrete random variable X , denoted E [ X ], is deFned as E [ X ]= X x i X x i P [ x i ]( 1 ) I DeFnition 2.13 p-28 The expected value of a continuous random variable X is then deFned as E [ X Z x X xf ( x ) dx (2) Charles B. Moss Expected Value and Moments

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Outline Expected Value Moments of a Distribution Empirical Moments Applications Bivariate Random Variables I Taking the die roll as an example, if we let each side be equally likely the expected value of the roll of a fair die is E [ x ]= 6 X i =1 iP [ i ]=1 1 6 +2 1 6 +3 1 6 +4 1 6 +5 1 6 +6 1 6 =3 1 2 (3) I This result points out an interesting fact about the expected value, namely that the expected value need not be an element o fthesamp leset . Charles B. Moss Expected Value and Moments
Outline Expected Value Moments of a Distribution Empirical Moments Applications Bivariate Random Variables I Suppose we weight the die so that it is no longer fair.

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This note was uploaded on 07/15/2011 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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Slides05-2010 - Outline Expected Value Moments of a Distribution Expected Value and Moments Charles B Moss Charles B Moss Expected Value and

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