Suppose \( X \) is a random variable taking possible values in \(\{1, 2, 3, \ldots\}\) and \(0 < P(X = 1) < 1\), and that \( X \) satisfies the memoryless property. Prove that \( X \) must be a geometrically distributed random variable for some parameter value \( p \).

Let X be the random variable having possible values {1,2,3...} and 0<p<1X satisfies the…

Answered: Suppose X is a random variable taking…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose X is a random variable taking possible values in {1, 2, 3,... } and 0 < P(X = 1) < 1, and that X satisfies the memoryless property. Prove that X must be a geometrically distributed random variable for some parameter value p.