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Question
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -3 | -1 | 0 | 1 | 3 |
| pi : | 0.05 | 0.45 | 0.20 | 0.25 | 0.05 |
Solution
| xi | pi | pixi | pixi2 |
| -3 | 0.05 | -0.15 | 0.45 |
| -1 | 0.45 | -0.45 | 0.45 |
| 0 | 0.20 | 0 | 0
|
| 1 | 0.25 | 0.25 | 0.25 |
| 3 | 0.05 | 0.15 | 0.45 |
| `∑`pixi = -0.2 | `∑`pixi2=1.6 |
\[\text{ Mean } = \sum p_i x_i = - 0 . 2\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean} \right)^2 \]
\[ = 1 . 6 - \left( - 0 . 2 \right)^2 \]
\[ = 1 . 56\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance} }\]
\[ = \sqrt{1 . 56}\]
\[ = 1 . 249\]
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