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If Y has a geometric distribution with success probability

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

Solution for problem 76E 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 76E

Problem 76E

If Y has a geometric distribution with success probability .3, what is the largest value, y0, such that P(Y > y0) .1?

Step-by-Step Solution:
Step 1 of 3

Solution 76E

Step1 of 2:

We have random variable ‘Y’ it follows geometric distribution with parameter ‘p = 0.3’.

Then the probability mass function of geometric distribution is given by:

Where,

x = random variable

p = probability of success(Parameter)

n = sample size

We need to find the largest value of such that P(Y > ) = 0.1.


Step2 of 2:

We have p = 0.3 then q = 1 - p

                                      = 1 - 0.3

                                      = 0.7

 

                       

We need to find the value of such that:

       

Apply natural log on both side we get

       

       

                 

                 

Hence, the largest value of  is 6.4570.


 

Step 2 of 3

Chapter 3, Problem 76E is Solved
Step 3 of 3

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

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. The answer to “If Y has a geometric distribution with success probability .3, what is the largest value, y0, such that P(Y > y0) ? .1?” is broken down into a number of easy to follow steps, and 23 words. This full solution covers the following key subjects: distribution, geometric, largest, Probability, success. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The full step-by-step solution to problem: 76E from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. Since the solution to 76E from 3 chapter was answered, more than 500 students have viewed the full step-by-step answer.

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If Y has a geometric distribution with success probability