Let X1 and X2 be independent, each with unknown
a. Let
b. Let
c. Let
d. For what values of µ does
e. For what values of µ does
a.
Find the bias, variance and mean squared error of
Answer to Problem 3E
The bias of
The variance of
The mean square error of
Explanation of Solution
Given info:
The random variables
Calculation:
Bias:
Assume that
Mean squared error:
The mean squared error (MSE) of
The mean of
Substitute
The bias of
Thus, the bias of
The variance of
Substitute
Substitute
Thus, the variance of
The mean squared error of
Then,
Thus, the mean square error of
b.
Find the bias, variance and mean squared error of
Answer to Problem 3E
The bias of
The variance of
The mean square error of
Explanation of Solution
Calculation:
The mean of
Substitute
The bias of
Thus, the bias of
The variance of
Substitute
Substitute
Thus, the variance of
The mean squared error of
Then,
Thus, the mean square error of
c.
Find the bias, variance and mean squared error of
Answer to Problem 3E
The bias of
The variance of
The mean square error of
Explanation of Solution
Calculation:
The mean of
Substitute
The bias of
Thus, the bias of
The variance of
Substitute
Substitute
Thus, the variance of
The mean squared error of
Then,
Thus, the mean square error of
d.
Find the values of
Answer to Problem 3E
The values of
Explanation of Solution
Calculation:
The mean square error of
The MSE of
On simplification,
That is,
Implies,
Thus, the values of
e.
Find the values of
Answer to Problem 3E
The values of
Explanation of Solution
Calculation:
The mean square error of
The MSE of
On simplification,
That is,
Implies,
Thus, the values of
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Chapter 4 Solutions
Statistics for Engineers and Scientists
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