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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

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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 3E

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.

  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 3

Chapter 4.9, Problem 3E is Solved
Step 3 of 3

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

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