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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.9 - Problem 3e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.9 - Problem 3e

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# Let X1 and X2 be independent, each with unknown mean µ and ISBN: 9780073401331 38

## Solution for problem 3E Chapter 4.9

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:

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

Step 3 of 3

##### ISBN: 9780073401331

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