21 10871092 neveu j 1975 discrete parameter

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Unformatted text preview: e that the variance of the uniform distribution will only depend on the length of the interval. To see that it will be a multiple of (b a)2 note that Z = X/(b a) is uniform on [ 1/2, 1/2] and then use part (d) of Theorem A.3 to conclude var (X ) = (b a)2 var (Z ). Of course one needs calculus to conclude that var (Z ) = 1/12. Generating functions will be used at several points in the text. If pk = P (X = k ) is the distribution of X then the generating function is (x) = P1 P1 k (1) = k=0 pk = 1. Di↵erentiating (and not worrying about the k=0 pk x . detail of interchanging the sum and th...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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