Integral Identities for Random Variables |
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Authors: | Edward B Rockower |
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Institution: | Department of Operations Research , Naval Postgraduate School , Monterey , California , 93943 , USA |
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Abstract: | Using a general method for deriving identities for random variables, we find a number of new results involving characteristic functions and generating functions. The method is simply to promote a parameter in an integral relation to the status of a random variable and then take expected values of both sides of the equation. Results include formulas for calculating the characteristic functions for x 2, √x, 1/x, x 2 + x, R 2 = x 2 + y 2, and so forth in terms of integral transforms of the characteristic functions for x and (x, y), and so forth. Generalizations to higher dimensions can be obtained using the same method. Expressions for inverse/fractional moments, E{n!}, and so forth are also presented, demonstrating the method. |
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Keywords: | Evidence Paradox |
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