Homework Help is Here – Start Your Trial Now!
Math
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

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)
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...
See similar textbooks
icon
Related questions
Question

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

Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer