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Expand Your Knowledge: Linear
Norb and Gary are entered in a local golf tournament. Both have played the local course many times. Their scores are random variables with the following means and standard deviations.
Norb.
In the tournament. Norb and Gary are not playing together, and we will assume their scores vary independently of each other.
(a) The difference between their scores is
(b) The average of their scores is
(c) The tournament rules have a special handicap system for each player. For Norb. the handicap formula is
(d) For Gary, the handicap formula is
(a)

The mean, variance and standard deviation for the provided linear combination W.
Answer to Problem 19P
Solution: The mean
Explanation of Solution
Given: The provided mean and standard deviation of random variables
The difference between the scores is,
Calculation: The general formula for the linear combination of random variables is as follows,
Now, comparing the provided linear combination of scores with the above formula as:
Now, the combined mean of the provided score can be obtained as:
Now, the combined variance can be obtained as:
The standard deviation can be obtained as:
Hence, the mean is 15, the variance is 208 and the standard deviation is 14.4.
(b)

The mean, variance and standard deviation for the provided linear combination W.
Answer to Problem 19P
Solution: The mean
Explanation of Solution
Given: The provided mean and standard deviation of random variables
The average of the scores is,
Calculation: The general formula for the linear combination of random variables is as follows,
Now, comparing the provided linear combination of scores with the above formula as:
Now, the combined mean of the provided score can be obtained as:
Now, the combined variance can be obtained as:
The standard deviation can be obtained as:
Hence, the mean is 107.50, the variance is 52 and the standard deviation is 7.2.
(c)

The mean, variance and standard deviation for the provided linear function L.
Answer to Problem 19P
Solution: The mean
Explanation of Solution
Given: The provided mean and standard deviation of random variable
For Norb, the handicap formula is as follows,
Calculation: The general formula for the linear function of a random variable is as follows:
Now, comparing the provided linear handicap formula with the above linear formula as:
Now, the mean of the provided linear function can be obtained as:
Now, the variance can be obtained as:
The standard deviation can be obtained as:
Hence, the mean is 90, the variance is 92.16 and the standard deviation is 9.6.
(d)

The mean, variance and standard deviation for the provided linear function L.
Answer to Problem 19P
Solution: The mean
Explanation of Solution
Given: The provided mean and standard deviation of random variable
For Gary, the handicap formula is as follows,
Calculation: The general formula for the linear function of a random variable is as follows:
Now, comparing the provided linear handicap formula with the above linear formula as:
Now, the mean of the provided linear function can be obtained as:
Now, the variance can be obtained as:
The standard deviation can be obtained as:
Hence, the mean is 90, the variance is 57.76 and the standard deviation is 7.6.
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Chapter 6 Solutions
Understanding Basic Statistics
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