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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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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