Concept explainers
(a)
Calculate the mean and variance.
(a)
Explanation of Solution
The probability distribution of random variable X is shown below:
Table 1
X | -2 | 5 | 7 | 8 |
P(X) | 0.59 | 0.15 | 0.25 | 0.01 |
The mean value of the probability distribution of X is calculated as follows:
The mean value is 1.40.
The variance of the probability distribution of X is calculated as follows:
The variance is 17.04.
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 Y is equal to 5X is shown in the below table:
X | -2 | 5 | 7 | 8 |
Y | -10 | 25 | 35 | 40 |
P(Y) | 0.59 | 0.15 | 0.25 | 0.01 |
(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 7.
The variance of the probability distribution of Y is calculated as follows:
The variance is 426.
(d)
The expected value and variance of Y.
(d)
Explanation of Solution
The expected value of Y from Parameter X is calculated as follows:
The expected value is 7.
The variance of Y from Parameter X is calculated as follows:
The variance is 426.
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Chapter 7 Solutions
Statistics for Management and Economics (Book Only)
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