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Question
Find the mean and standard deviation of each of the following probability distributions:
| xi : | 2 | 3 | 4 |
| pi : | 0.2 | 0.5 | 0.3 |
Solution
| xi | pi | pixi | pixi2 |
| 2 | 0.2 | 0.4 | 0.8 |
| 3 | 0.5 | 1.5 | 4.5 |
| 4 | 0.3 | 1.2 | 4.8 |
| `∑`pixi = 3.1
|
`∑`pixi2 = 10.1
|
\[\text{ Mean } = \sum p_i x_i = 3 . 1\]
\[\text{ Variance} = \sum p_i {x_i}^2 - \left( \text{ Mean} \right)^2 \]
\[ = 10 . 1 - \left( 3 . 1 \right)^2 \]
\[ = 10 . 1 - 9 . 61\]
\[ = 0 . 49\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance}}\]
\[ = \sqrt{0 . 49}\]
\[ = 0 . 7\]
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