×
Log in to StudySoup

Forgot password? Reset password here

Let X1 and X2 be independent, each with unknown mean µ and

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

Solution for problem 3E Chapter 4.9

Statistics for Engineers and Scientists | 4th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 0 372 Reviews
25
2
Problem 3E

Let X1 and X2 be independent, each with unknown mean µ and known variance  =1.

a. Let  Find the bias, variance, and mean squared error of   

b. Let   Find the bias, variance, and mean squared error of

c. Let  Find the bias, variance, and mean squared error of  

d. For what values of does have smaller mean squared error than?

e. For what values of n does  have smaller mean squared error than

Step-by-Step Solution:

Answer:

Step 1 of 5:

Given,  let  and be independent, with unknown mean  and known variance = 1.

Let, = then the claim is to find the bias, variance and mean squared error (MSE)  of

             Bias of  = E( ) -

            We know that mean of   is E( ) and variance of  is V( )

E( ) =  

               =  

               =  

              =

Hence, mean of  is 

The bias of  = E( ) -

                       = -

              = 0

Therefore, The bias of  is 0.

variance of  is V( )

V( ) =

            =  

           =  

           =  

We have, = 1

Therefore, V( ) =

The mean square error of  = V( ) + (bias

                   = + 0

               =

Hence, the mean square error of  is

Step 2 of 5:

Let, = then the claim is to find the bias, variance and mean squared error (MSE)  of 

             Bias of  = E( ) -

            We know that mean of   is E( ) and variance of  is V( )

E( ) =  

               =  

                 =  

              =

Hence, mean of  is

The bias of  = E( ) -

                       = -

                   = 0

Therefore, The bias of  is 0.

variance of  is V( )

V( ) =

            =  

           =  

           =  

We have, =

Therefore, V( ) =

The mean square error of  = V( ) + (bias

                  = + 0

              =  

Hence, the mean square error of  is  

Step 3 of 3

Chapter 4.9, Problem 3E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Let X1 and X2 be independent, each with unknown mean µ and

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

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here