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A radioactive mass emits particles according to a Poisson

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

Solution for problem 8E Chapter 4.7

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 8E

A radioactive mass emits particles according to a Poisson process at a mean rate of 2 per second.

Let T be the waiting time, in seconds, between Emissions.

a. What is the mean waiting time?

b. What is the median waiting time?

c. Find P(T > 2).

d. Find P(T<0.1).

e. Find P(0.3<T<1.5).

f. If 3 seconds have elapsed with no emission, what is the   probability that there will be an emission within the next second?

Step-by-Step Solution:

Step 1 of 7</p>

Here given radioactive mass emits the particles according to the poisson distribution with mean

The pmf of exponential distribution is

The CDF of exponential distribution is

 

Let T be the waiting time between emissions

Here T follows exponential distribution with parameter

Step 2 of 7</p>

a) We have to find the mean of the waiting time

The mean of exponential distribution is

                                                                       =0.5

Hence the mean of the waiting time is 0.5 seconds

Step 3 of 7</p>

b) We have to find median waiting time

Let a be the median

Then

         =0.5

                =0.5

                         

                          0.3466

Hence the median waiting time is 0.3466

Step 4 of 7</p>

c) we have to find P(T>2)

P(T>2)=

            =1-(

                                                                       =

 =0.0183

Hence P(T>2) is 0.0183

Step 5 of 7

Chapter 4.7, Problem 8E is Solved
Step 6 of 7

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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