Concept explainers
(a)
Calculate the mean and standard deviation.
(a)
Explanation of Solution
The probability distribution of the random variable X is shown below:
Table 1
X | 0 | 1 | 2 | 3 |
P(X) | 0.4 | 0.3 | 0.2 | 0.1 |
The mean value of the probability distribution of X is calculated as follows:
The mean value is 1.
The standard deviation of probability distribution of X is calculated as follows:
The standard deviation is 1.
Probability distribution: The probability distribution shows the probabilities of incidence of different likely outcomes in a test.
(b)
The probability distribution of Y.
(b)
Explanation of Solution
The probability distribution of Y where
X | 0 | 1 | 2 | 3 |
Y | 2 | 5 | 8 | 11 |
P(Y) | 0.4 | 0.3 | 0.2 | 0.1 |
(c)
The mean and variance of Y.
(c)
Explanation of Solution
The mean value of the probability distribution of Y is calculated as follows:
The mean value is 5.
The standard deviation of the probability distribution of Y is calculated as follows:
The standard deviation is 3.
(d)
The mean, variance, and standard deviation.
(d)
Explanation of Solution
The mean value is calculated as follows:
The mean value is 5.
Variance and standard deviation are calculated as follows:
The variance is 9 and standard deviation is 3. The parameters are identical.
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Chapter 7 Solutions
EBK MINDTAP FOR KELLER'S STATISTICS FOR
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