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प्रश्न
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -5 | -4 | 1 | 2 |
| pi : | \[\frac{1}{4}\] | \[\frac{1}{8}\] | \[\frac{1}{2}\] | \[\frac{1}{8}\] |
उत्तर
| xi | pi | pixi | pixi2 |
| -5 | `1/4` | `-5/4` |
`25/4` |
| -4 | `1/8` | `-4/8` | `16/8` |
| 1 | `1/2` | `1/2` | `1/2` |
| 2 | `1/8` | `2/8` | `4/8` |
|
`∑`pixi=1 |
\[\sum\nolimits_{}^{}\]pixi2=\[\frac{74}{8}\]
|
\[\text{ Mean } = \sum p_i x_i = - 1\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean } \right)^2 \]
\[ = \frac{74}{8} - \left( - 1 \right)^2 \]
\[ = 9 . 25 - 1\]
\[ = 8 . 25\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance } }\]
\[ = \sqrt{8 . 25}\]
\[ = 2 . 872\]
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