Concept explainers
a.
Prove that
a.
Explanation of Solution
Calculation:
Binomial probability distribution:
A discrete random variable Y is said to follow a Binomial distribution with mean
The mean and variance of Y are
Beta distribution:
A continuous random variable Y is said to follow a Beta distribution with parameters
The mean and variance of Y are
The conditional expectation of any real valued function
It is given that the conditional distribution of Y given p follows Binomial distribution with parameters n and p where p follows Beta distribution with parameters
Thus, the expected value of the conditional distribution of
For two random variables
Hence,
Therefore, it is proved that
b.
Prove that
b.
Explanation of Solution
Calculation:
For two random variables
From Part (a), it is obtained that
Hence,
Therefore, it is proved that
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Chapter 5 Solutions
Mathematical Statistics with Applications
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