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Question
Find the mean and standard deviation of each of the following probability distribution :
| xi : | 1 | 2 | 3 | 4 |
| pi : | 0.4 | 0.3 | 0.2 | 0.1 |
Solution
| xi | pi | pixi | pixi2 |
| 1 | 0.4 | 0.4 | 0.4 |
| 2 | 0.3 | 0.6 | 1.2 |
| 3 | 0.2 | 0.6 | 1.8 |
| 4 | 0.1 | 0.4 | 1.6 |
| `∑`pixi = 2 | `∑`pixi2=5
|
\[\text{ Mean } = \sum p_i x_i = 2\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean} \right)^2 \]
\[ = 5 - 2^2 \]
\[ = 1\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance } }\]
\[ = \sqrt{1}\]
\[ = 1\]
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