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Slides05-2010

# Slides05-2010 - Outline Expected Value Moments of a...

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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 The random variable can also be described using a statistic. One basic statistic encountered by students in statistics courses is the mean of a random variable. Definition 2.12 p-28 The expected value (expectation or mean) of a discrete random variable X , denoted E [ X ], is defined as E [ X ] = x i X x i P [ x i ] (1) Definition 2.13 p-28 The expected value of a continuous random variable X is then defined as E [ X ] = 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 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 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) This result points out an interesting fact about the expected value, namely that the expected value need not be an element of the sample set. Charles B. Moss Expected Value and Moments
Outline Expected Value Moments of a Distribution Empirical Moments Applications Bivariate Random Variables Suppose we weight the die so that it is no longer fair.

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