a.
Prove that the marginal distribution of
a.
Explanation of Solution
Calculation:
Consider that
Then, the marginal probability
Exponential distribution:
A random variable Y is said to follow the exponential distribution with mean 1, if and only if the probability density function of Y is
Consider that
Thus, using the joint probability density functions of
Thus, it is proved that the marginal distribution of
b.
Find the marginal distribution of
b.
Answer to Problem 65E
The marginal distribution of
Explanation of Solution
Calculation:
Consider that
Thus, using the joint probability density functions of
Thus, the marginal distribution of
c.
Prove that
c.
Explanation of Solution
The two continuous random variables
Substitute
That is,
From Part (a) and Part (b), the marginal distribution of
Here, the ranges of
That is,
Thus, it is proved that
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Chapter 5 Solutions
Mathematical Statistics with Applications
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