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 have
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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Related Book For
Introduction To Probability Volume 2
ISBN: 9781118123331
1st Edition
Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
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