Concept explainers
a.
Use the binomial formula to prove that
a.
Answer to Problem 135E
It is proved that
Explanation of Solution
The random variable
The random variable
Consider,
It is noted that parameter
Therefore, it is proved that
b.
Use the relationship between the beta distribution function and sum of binomial probabilities given in Exercise 4.134. If k is an integer between 1 and
b.
Answer to Problem 135E
It is deduced that
Explanation of Solution
Consider L.H.S:
Where X is a beta distribution with parameters
Thus, it is deduced that
c.
If k is any integer between 1 and
Interpret the results.
c.
Answer to Problem 135E
It is proved that
Explanation of Solution
One has to prove that
Consider,
Again,
It is noted that the integrands for
Hence, it is proved that
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Chapter 4 Solutions
Mathematical Statistics with Applications
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