Let X have the conditional geometric pmf (1)x1, x = 1, 2, . . ., where
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Let X have the conditional geometric pmf θ(1−θ)x−1, x = 1, 2, . . ., where θ is a value of a random variable having a beta pdf with parameters α and β. Show that the marginal (unconditional) pmf of X is
If α = 1, we obtain
which is one form of Zipf ’s law.
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T(a + 3)(a + 1)(3+x-1) r(a)(3)(a +3+x) x = 1,2,....
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Related Book For
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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