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Question
Find the mean and standard deviation of each of the following probability distribution:
| xi : | 1 | 3 | 4 | 5 |
| pi: | 0.4 | 0.1 | 0.2 | 0.3 |
Solution
| xi | pi | pixi | pixi2 |
| 1 | 0.4 | 0.4 | 0.4 |
| 3 | 0.1 | 0.3 | 0.9 |
| 4 | 0.2 | 0.8 | 3.2 |
| 5 | 0.3 | 1.5 | 7.5 |
| `∑` pixi = 3
|
`∑`pixi2=12 |
\[\text{ Mean } = \sum p_i x_i = 3\]
\[\text{ Variance } = \sum p_i {x_i}^2{}_{} - \left( \text{ Mean} \right)^2 \]
\[ = 12 - 3^2 \]
\[ = 3\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance}}\]
\[ = \sqrt{3}\]
\[ = 1 . 732\]
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