Concept explainers
Given the following
- Compute the expected value for each distribution.
- Compute the standard deviation for each distribution.
- Compare the results of distributions A and B.
(a)
To find: The expected values for both the distributions.
Answer to Problem 5.1LB
The expected values are 1 and 3 respectively.
Explanation of Solution
Given:
The probability distributions are:
Distribution A | Distribution B | ||
0 | 0.5 | 0 | 0.05 |
1 | 0.2 | 1 | 0.1 |
2 | 0.15 | 2 | 0.15 |
3 | 0.1 | 3 | 0.2 |
4 | 0.05 | 4 | 0.5 |
Formula used:
The formula to compute the expected mean is:
Here,
The formula to compute the standard deviation is:
Calculation:
The expected values for both the distributions can be calculated as:
Distribution A:
Distribution B:
Thus, the required expected values are 1 and 3 respectively.
(b)
To find: The standard deviation for each distribution.
Answer to Problem 5.1LB
The standard deviations are 1.225 and 1.225 respectively.
Explanation of Solution
The standard deviation for each distribution can be computed as:
Distribution A:
Distribution B:
Thus, the required standard deviations are 1.225 and 1.225 respectively.
(c)
To compare: The provided distributions.
Explanation of Solution
From the above two parts, it is clear that the mean of distribution B is greater than the mean of distribution B but there is no difference in the standard deviation of two distributions.
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