Concept explainers
a.
Verify that the distribution
a.
Explanation of Solution
The distribution for
For
For
For
Substitute
b.
Verify that the distribution function of
b.
Explanation of Solution
From Part (a), the distribution function of
Consider the following:
For
For
For
The distribution function for
It is said to be pivotal quantity for
Since the above expression is independent of
c.
i Calculate the value of
ii Construct 95% confidence interval for
c.
Answer to Problem 132SE
i The value of
ii The 95% confidence interval for
Explanation of Solution
The distribution function for
i The value of k is calculated as follows:
Therefore, the value of
ii
The 95% confidence interval for
The 95% confidence interval for
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Chapter 8 Solutions
Mathematical Statistics with Applications
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