Let X be a geometric distribution with parameter 0 < p < 1. (a) Show that P(X > k) = (1 − p)^k for every k belongs to the set of natural numbers (b) Show that X is memoryless, i.e., P(X > k + ? |X > ?) = P(X > k) for all k, ? ∈ Natural numbers. (c) Show that geometrically distributed random variables are the only natural number random variables that are memoryless. Hint: Suppose X takes values in natural numbers and is memoryless. View P(X > k) and use the law of total probability

Let X be a geometric distribution with parameter 0 < p < 1. (a) Show that P(X > k) = (1 − p)^k for every k belongs to the set of natural numbers (b) Show that X is memoryless, i.e., P(X > k + ? |X > ?) = P(X > k) for all k, ? ∈ Natural numbers. (c) Show that geometrically distributed random variables are the only natural number random variables that are memoryless. Hint: Suppose X takes values in natural numbers and is memoryless. View P(X > k) and use the law of total probability

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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