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प्रश्न
Find the mean and standard deviation of each of the following probability distribution:
| xi : | −1 | 0 | 1 | 2 | 3 |
| pi : | 0.3 | 0.1 | 0.1 | 0.3 | 0.2 |
उत्तर
| xi | pi | pixi | pixi2 |
| -1 | 0.3 | -0.3 | 0.3
|
| 0 | 0.1 | 0 | 0 |
| 1 | 0.1 | 0.1 | 0.1 |
| 2 | 0.3 | 0.6 | 1.2 |
| 3 | 0.2 | 0.6 | 1.8 |
| `∑`pixi = 1 | `∑`pixi2=3.4
|
\[\text{ Mean } = \sum p_i x_i = 1\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean } \right)^2 \]
\[ = 3 . 4 - 1\]
\[ = 2 . 4\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance} }\]
\[ = \sqrt{2 . 4}\]
\[ = 1 . 549\]
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