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Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 3 - Problem 143e
Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 3 - Problem 143e

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# Refer to Exercise 3.142 (c). If the number of phone calls

ISBN: 9780495110811 47

## Solution for problem 143E Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Problem 143E

Problem 143E

Refer to Exercise 3.142 (c). If the number of phone calls to the fire department, Y , in a day has a Poisson distribution with mean 5.3, what is the most likely number of phone calls to the fire department on any day?

Reference

Let p(y) denote the probability function associated with a Poisson random variable with mean λ.

c Notice that the result in part (a) implies that Poisson probabilities increase for a while as y increases and decrease thereafter. Show that p(y) maximized when y = the greatest integer less than or equal to λ.

Step-by-Step Solution:

Solution

Step 1 of 1

We have to find the no.of phone calls per day to the fire department

Let Y is the no.of phone calls to the fire department

Here

Here given that Y is following poisson distribution with mean 5.3

The mean of the  poisson distribution is

We know that P(Y) is maximised when Y= greatest integer less than or equal to

Here

Then y should be less than and should be greatest integer

So y=5

Hence we can expect 5 phone calls per day to the fire department

Step 2 of 1

##### ISBN: 9780495110811

The full step-by-step solution to problem: 143E from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. Since the solution to 143E from 3 chapter was answered, more than 301 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Poisson, day, phone, calls, mean. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The answer to “Refer to Exercise 3.142 (c). If the number of phone calls to the fire department, Y , in a day has a Poisson distribution with mean 5.3, what is the most likely number of phone calls to the fire department on any day?ReferenceLet p(y) denote the probability function associated with a Poisson random variable with mean ?. c Notice that the result in part (a) implies that Poisson probabilities increase for a while as y increases and decrease thereafter. Show that p(y) maximized when y = the greatest integer less than or equal to ?.” is broken down into a number of easy to follow steps, and 95 words.

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