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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4 - Problem 29se
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4 - Problem 29se

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

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

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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:

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

##### 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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