In Section 5.2, we showed that the geometric distribution has the memoryless property, i.e. for any positive

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In Section 5.2, we showed that the geometric distribution has the memoryless property, i.e. for any positive integers n, k, we haveimage text in transcribed

Verify that the converse is true; that is, if a random variable Y on the nonnegative integers satisfies the above for all n and k, then the distribution of Y is geometric.
This type of a result, meaning a two-way implication, is called a characterization of the distribution.

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Introduction To Probability Volume 2

ISBN: 9781118123331

1st Edition

Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis

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