×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide

There are times when a shifted exponential model is

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 5E Chapter 3.2

Probability and Statistical Inference | 9th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

4 5 1 351 Reviews
12
0
Problem 5E

There are times when a shifted exponential model is appropriate. That is, let the pdf of X be

(a) Define the cdf of X.

(b) Calculate the mean and variance of X.

Step-by-Step Solution:
Step 1 of 3

Solution 5E

Step1 of 3:

We have A Exponential random variable X with pdf

 

We need to find,

(a) Define the cdf of X.

(b) Calculate the mean and variance of X.

Step2 of 3:

Let “X” be random variable which follows Exponential distribution with parameters .

That is X Exp()

The probability mass function of binomial distribution is given below

Where,

X = random variable

 = parameter

 = parameter

e = a constant it is approximately 2.7182.

a).

Consider,

To get a cdf of X we need to integrate above function with respect to x.

1).If X < then,

   

               =

               = 0.

2).If X then,

   

               =

          =  

          = [

          =

          =

          =

Hence, the cdf is given by

Step3 of 3: 

b).

Consider,

To get mean and variance of X we need to integrate above function with respect to x.

 

            =

            = []

 ...

Step 2 of 3

Chapter 3.2, Problem 5E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

There are times when a shifted exponential model is

×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
×
Reset your password