a.
Find the density
a.
Answer to Problem 76SE
The density function of
Explanation of Solution
Calculation:
From Theorem 6.5, the density function for kth order statistic,
It is known that, the density function of Uniform distribution over the interval
The density function for
b.
Find the value of
b.
Answer to Problem 76SE
The value of
Explanation of Solution
Calculation:
Consider,
This function
Therefore,
c.
Find the value of
c.
Answer to Problem 76SE
The value of
Explanation of Solution
Calculation:
Consider,
Therefore,
d.
Find the mean difference between two successive order statistics,
d.
Answer to Problem 76SE
The mean difference between two successive order statistics,
The expected order statistics are equally spaced.
Explanation of Solution
Calculation:
Consider,
This function is a constant for all k. Thus, the expected order statistics are equally spaced.
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Chapter 6 Solutions
Mathematical Statistics with Applications
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