Concept explainers
Let Y have probability density
a Show that Y has distribution function
b Show that Y/θ is a pivotal quantity.
c Use the pivotal quantity from part (b) to find a 90% lower confidence limit for θ.
a.
Verify that the distribution of Y is
Explanation of Solution
The distribution function for
The distribution functions for
The distribution functions for
Thus, the distribution of Y is obtained as
Hence, it is verified.
b.
Verify that
Explanation of Solution
From Part (a), the distribution of Y is obtained as
The distribution function for
It can be written as follows:
From the above expression, it is clear that the distribution function for
c.
Obtain 90% lower confidence limit for
Answer to Problem 44E
90% lower confidence limit for
Explanation of Solution
From Part (b), the distribution of Y is obtained as
Since 0.90 lies between 0 and
Thus, 90% lower confidence limit for
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Chapter 8 Solutions
EBK MATHEMATICAL STATISTICS WITH APPLIC
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