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Let X ~ Poisson(?).a. Show that if x is a positive

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 29SE Chapter 4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 29SE

Let  Poisson  .

a. Show that if  is a positive integer, then

\(\frac{P(X=x)}{P(Y=x-1)}=\frac{\lambda}{x}\)

b. Show that if  Poisson , the most probable value for  is the greatest integer less than or equal to . [Hint: Use part (a) to show that \(P(X=x) \geq P(X=x-1)\) if and only if \(x \leq \lambda\)].

Equation transcription:

Text transcription:

frac{P(X=x)}{P(Y=x-1)}=frac{\lambda}{x}

P(X=x) geq P(X=x-1)

x leq lambda

Step-by-Step Solution:

Answer:

Step 1 of 2:

(a)

In this question, we are asked to prove the following.

…………(1)

Where x is a positive integer and  is a parameter.

If  is a random variable whose distribution is poisson with parameter , then we can write

The probability mass function of a poisson random variable is defined by,

                                                        =    otherwise

                                     ………………..(2)

Replace  with in equation (2), we get

                                             ………………….(3)

 =

can be written as

 =

 =

Hence proved.


Step 2 of 2

Chapter 4, Problem 29SE is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 29SE from chapter: 4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “?Let Poisson .a. Show that if is a positive integer, then\(\frac{P(X=x)}{P(Y=x-1)}=\frac{\lambda}{x}\)b. Show that if Poisson , the most probable value for is the greatest integer less than or equal to . [Hint: Use part (a) to show that \(P(X=x) \geq P(X=x-1)\) if and only if \(x \leq \lambda\)].Equation transcription:Text transcription:frac{P(X=x)}{P(Y=x-1)}=frac{\lambda}{x}P(X=x) geq P(X=x-1)x leq lambda” is broken down into a number of easy to follow steps, and 54 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 29SE from 4 chapter was answered, more than 354 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: show, Integer, Poisson, most, less. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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Let X ~ Poisson(?).a. Show that if x is a positive