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Let Y denote a geometric random variable with probability

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 71E Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 71E

Problem 71E

Let Y denote a geometric random variable with probability of success p.

a Show that for a positive integer a,

P ( Y > a ) = qa .

b Show that for positive integers a and b,

P ( Y > a + b|Y > a) = qb = P(Y > b).

This result implies that, for example, P(Y > 7|Y > 2) = P(Y > 5). Why do you think this property is called the memoryless property of the geometric distribution?

c In the development of the distribution of the geometric random variable, we assumed that the experiment consisted of conducting identical and independent trials until the first success was observed. In light of these assumptions, why is the result in part (b) “obvious”?

Step-by-Step Solution:

Solution:

Step 1 of 4:

Let Y denote a geometric random variable  with probability of success P.

We have to show that

  1. For a positive integer a,

            P(Y>a) = .

      (b)  For positive integers a and b,

             P(Y>a+b/Y>a) = P(Y>b).

      (c)  Why is the result in part (b) is obvious.


Step 2 of 4

Chapter 3, Problem 71E is Solved
Step 3 of 4

Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

Since the solution to 71E from 3 chapter was answered, more than 1073 students have viewed the full step-by-step answer. The answer to “Let Y denote a geometric random variable with probability of success p.a Show that for a positive integer a,P ( Y > a ) = qa .b Show that for positive integers a and b,P ( Y > a + b|Y > a) = qb = P(Y > b).This result implies that, for example, P(Y > 7|Y > 2) = P(Y > 5). Why do you think this property is called the memoryless property of the geometric distribution?c In the development of the distribution of the geometric random variable, we assumed that the experiment consisted of conducting identical and independent trials until the first success was observed. In light of these assumptions, why is the result in part (b) “obvious”?” is broken down into a number of easy to follow steps, and 120 words. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. This full solution covers the following key subjects: geometric, random, show, result, success. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The full step-by-step solution to problem: 71E from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM.

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Let Y denote a geometric random variable with probability