×
Log in to StudySoup
Get Full Access to A First Course In Probability - 9 Edition - Chapter 4 - Problem 57p
Join StudySoup for FREE
Get Full Access to A First Course In Probability - 9 Edition - Chapter 4 - Problem 57p

Already have an account? Login here
×
Reset your password

Suppose that the number of accidents occurring on a

A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross ISBN: 9780321794772 63

Solution for problem 57P Chapter 4

A First Course in Probability | 9th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross

A First Course in Probability | 9th Edition

4 5 1 314 Reviews
17
2
Problem 57P

Problem 57P

Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with parameter λ = 3.

(a) Find the probability that 3 or more accidents occur today,

(b) Repeat part (a) under the assumption that at least 1 accident occurs today.

Step-by-Step Solution:
Step 1 of 3

Solution 57P

Step1 of 3:

From the given problem we have a random variable ‘X’ it presents the number of accidents occurring on a highway each day. Here X follows poisson distribution with parameter

Here our goal is:

a). We need to find the probability that 3 or more accidents occur today.

b). We need to find the probability that at least 1 accident occurs today.


Step2 of 3:

a).

Here the random variable X follows poisson distribution with parameter  Then, the probability mass function of poisson distribution is:

                  

Consider,

                       

                                       

                               

                               

                                         

                                         

                                         

Therefore, The probability that 3 or more accidents occur today is 0.5767.


Step3 of 3:

b).

The probability that at least 1 accident occurs today is:

                                       

Where,

                                                      [from part (a)]

                                                   

                                                                         

                                                                                

                                                       

                                                                       

Therefore, P(X1) = 0.9502.

Now,

 

                                 

Therefore, The probability that at least 1 accident occurs today is 0.6069.


Step 2 of 3

Chapter 4, Problem 57P is Solved
Step 3 of 3

Textbook: A First Course in Probability
Edition: 9
Author: Sheldon Ross
ISBN: 9780321794772

This full solution covers the following key subjects: accidents, today, parameter, day, Find. This expansive textbook survival guide covers 4 chapters, and 469 solutions. The full step-by-step solution to problem: 57P from chapter: 4 was answered by , our top Statistics solution expert on 08/11/17, 08:57AM. Since the solution to 57P from 4 chapter was answered, more than 781 students have viewed the full step-by-step answer. A First Course in Probability was written by and is associated to the ISBN: 9780321794772. This textbook survival guide was created for the textbook: A First Course in Probability , edition: 9. The answer to “Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with parameter ? = 3.(a) Find the probability that 3 or more accidents occur today,________________(b) Repeat part (a) under the assumption that at least 1 accident occurs today.” is broken down into a number of easy to follow steps, and 45 words.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Suppose that the number of accidents occurring on a