a.
Find the marginal density
a.
Answer to Problem 27E
The marginal density function for
Explanation of Solution
Calculation:
Consider that
Then, the marginal probability functions of
The range of
Hence, the marginal probability density function for
Thus, the marginal density function for
In similar way, the marginal probability density function for
Thus, the marginal density function for
b.
Find the value of
b.
Answer to Problem 27E
The value of
Explanation of Solution
Conditional distribution and density function:
Consider that
Now, the conditional distribution function of
Now, for any
Similarly, for any
Hence,
Thus, value of
c.
Find the conditional density function of
c.
Answer to Problem 27E
The conditional density function of
Explanation of Solution
Calculation:
From Part (a), the marginal density function for
Hence, using the joint probability density function of
Thus, the conditional density function of
d.
Find the conditional density function of
d.
Answer to Problem 27E
The conditional density function of
Explanation of Solution
Calculation:
From Part (a), the marginal density function for
Hence, using the joint probability density function of
Thus, the conditional density function of
e.
Find the value of
e.
Answer to Problem 27E
The value of
Explanation of Solution
Using the joint probability density function of
Hence,
Thus, value of
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Chapter 5 Solutions
Mathematical Statistics with Applications
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