Concept explainers
(a)
To find: The variance and standard deviation of the random variable Z.
(a)
Answer to Problem 73E
Solution: The variance and standard deviation of random variable Z are 1600 and 40, respectively.
Explanation of Solution
Calculation: Consider X, Y, and Z to be the random variables with averages
Substitute the values in the above formula:
The standard deviation can be calculated as follows:
Substitute the values in the above formula:
(b)
To find: The variance and standard deviation of the random variable Z.
(b)
Answer to Problem 73E
Solution: The variance and standard deviation of random variable Z are 2304 and 48, respectively.
Explanation of Solution
Calculation: Consider X, Y, and Z to be the random variables with averages
Substitute the values in the above formula:
The standard deviation can be calculated as follows:
Substitute the values in the above formula:
(c)
To find: The variance and standard deviation of the random variable Z.
(c)
Answer to Problem 73E
Solution: The variance and standard deviation of random variable Z are 112 and 10.6, respectively.
Explanation of Solution
Calculation: Consider X, Y, and Z to be the random variables with averages
Substitute the values in the above formula:
The standard deviation can be calculated as follows:
Substitute the values in the above formula:
(d)
To find: The variance and standard deviation of the random variable Z.
(d)
Answer to Problem 73E
Solution: The variance and standard deviation of random variable Z are 48 and 6.9, respectively.
Explanation of Solution
Calculation: Consider X, Y, and Z to be the random variables with averages
Substitute the values in the above formula:
The standard deviation can be calculated as follows:
Substitute the values in the above formula:
(e)
To find: The variance and standard deviation of the random variable Z.
(e)
Answer to Problem 73E
Solution: The variance and standard deviation of random variable Z are 192 and 13.85, respectively.
Explanation of Solution
Calculation:
Substitute the provided values in the above formula:
Consider X, Y, and Z to be the random variables with averages
Substitute the values in the above formula:
The standard deviation can be calculated as follows:
Substitute the values in the above formula:
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Chapter 4 Solutions
Introduction to the Practice of Statistics
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