Let X denote a random variable such that K(t) = E(t X ) exists for all real

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Let X denote a random variable such that K(t) = E(t^X) exists for all real values of t in a certain open interval that includes the point t = 1. Show that K(m)(1) is equal to the mth factorial moment E[X(X − 1) · · · (X − m + 1)].

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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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Question Posted: Oct 13, 2022 02:24 AM

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Let X denote a random variable such that K(t) = E(t X ) exists for all real

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We have that Kt EtX for all t in some open interval that includes t 1 We want ...View the full answer

Introduction To Mathematical Statistics

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