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
Want to see more full solutions like this?
Chapter 8 Solutions
Mathematical Statistics with Applications
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,