a.
Find the marginal density
a.
Answer to Problem 149SE
The marginal probability density function of
Explanation of Solution
Calculation:
Consider that
Then, the marginal probability functions of
Thus, marginal probability density function of
Thus, the marginal probability density function of
Similarly, marginal probability density function of
Thus, the marginal density function for
b.
Find the value of
b.
Answer to Problem 149SE
The value of
Explanation of Solution
Calculation:
Conditional distribution and density function:
Consider that
Now, the conditional distribution function of
Now, for any
Similarly, for any
From Part (a), it is found that the marginal probability density function of
Hence, using the marginal probability functions the required probability is obtained as,
Thus, the value of
c.
Find the conditional density
c.
Answer to Problem 149SE
The conditional density
Explanation of Solution
Using the joint probability function of
Thus, the conditional density
d.
Find the value of
d.
Answer to Problem 149SE
The value of
Explanation of Solution
Calculation:
From Part (C), it is obtained that the conditional density
Hence, the required probability is obtained as,
Thus, the value of
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Chapter 5 Solutions
Mathematical Statistics with Applications
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning