Concept explainers
(a)
To find: The formula for the mean and standard deviation of
(a)
Answer to Problem 49UYK
Solution: The formula for mean of
Similarly, the formula for mean of
The formula for standard deviation of
Similarly, the formula for standard deviation of
Explanation of Solution
Calculation: The formula for mean of population proportion
The formula for standard deviation of population proportion
So, the mean for
(b)
To find: The mean of difference
(b)
Answer to Problem 49UYK
Solution: The mean of D is
Explanation of Solution
Calculation: The mean of the sum of two random variables is the sum of the individual means of those random variables.
The formula for mean of the sum of two random variables X and Y is as follows:
where
So, the mean of D is calculated as follows:
From part (a), the value of
On substituting the values,
Hence, the required mean of the difference is
(c)
To find: The variance of D.
(c)
Answer to Problem 49UYK
Solution: The variance of D is
Explanation of Solution
Calculation: The variance of the sum of two random variables will be equal to the sum of the individual variances and twice the
where
But the variables are independent, so
Hence, the required variance of the difference is
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Chapter 8 Solutions
INTRO.TO PRAC.OF STATISTICS (W/SAPLING)
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