a.
Find the cumulative distribution
a.
Answer to Problem 22SE
The cumulative distribution function of X is,
Explanation of Solution
Given info:
The random variable X follows Pareto distribution with parameters
Calculation:
For a continuous random variable with probability density function
From the probability density function of the Pareto distribution it can be seen that if
For
For
Substitute
It can be concluded that the cumulative distribution of X is,
Hence, the result.
b.
Find the value of
b.
Answer to Problem 22SE
The value of mean is
Explanation of Solution
Calculation:
For a continuous random variable with probability density function
Substitute
Thus, the value of mean is,
c.
Find the value of
c.
Answer to Problem 22SE
The variance is
Explanation of Solution
Calculation:
For a continuous random variable with probability density function
Substitute
Thus, the value of variance is,
d.
Show that
d.
Answer to Problem 22SE
The mean does not exist for
Explanation of Solution
Calculation:
For a continuous random variable with probability density function
Substitute
It diverges, since
Thus, the value of mean does not exist for
d.
Show that
d.
Answer to Problem 22SE
The variance does not exist for
Explanation of Solution
Calculation:
For a continuous random variable with probability density function
Substitute
It diverges, since
Thus, the value of variance does not exist for
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Chapter 4 Solutions
Statistics for Engineers and Scientists
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