Concept explainers
a.
Find the density
a.
Answer to Problem 2E
The density function for
Explanation of Solution
Calculation:
From the given information, the probability density function for Y is
The distribution function for Y is,
From the given information, the random variable
Consider the distribution function for
Limits for the random variable U1:
The range for the random variable Y is from ̶ 1 to 1 and
For Y= ̶ 1, the value of U1 is ̶ 3.
For
Hence, the range for the random variable U1 is from ̶ 3 to 3.
The probability density function for
Thus, the density function for
b.
Find the density function for
b.
Answer to Problem 2E
The density function for
Explanation of Solution
Calculation:
From the given information,
Consider the distribution function for
Limits for the random variable U2:
The
For Y= ̶ 1, the value of U2 is 4.
For
Hence, the range for the random variable U2 is from 2 to 4.
The probability density function for
Thus, the density function for
c.
Find the density function for
c.
Answer to Problem 2E
The density function for
Explanation of Solution
Calculation:
From the given information,
Consider the distribution function for
The probability density function for
Thus, the density function for
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Chapter 6 Solutions
Mathematical Statistics with Applications
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