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WEB-APPENDIX L: SOME ELEMENTARY CONCEPTS... > L.2 MEASURES OF DISPERSION FOR RANDO...

L.2 MEASURES OF DISPERSION FOR RANDOM VARIABLES

We next look at measures of dispersion for random variables, defining first the variance,

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Since the term E(r) inside the braces can be treated as a constant,

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We then define standard deviation as:

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The mean, variance, and standard deviation may be readily computed for a discrete probability distribution using the computational formulas:

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and

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where i indicates the values taken on by r and pi refers to the probability outcome i will be realized. For the small table of rp above we have:

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Thus,

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Another useful property of variance and standard deviation is that

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