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Question
Find the mean and standard deviation of each of the following probability distribution :
| xi: | 0 | 1 | 3 | 5 |
| pi : | 0.2 | 0.5 | 0.2 | 0.1 |
Solution
| xi | pi | pixi | pixi2 |
| 0 | 0.2 | 0 | 0 |
| 1 | 0.5 | 0.5 | 0.5 |
| 3 | 0.2 | 0.6 | 1.8 |
| 5 | 0.1 | 0.5 | 2.5 |
| `∑`pixi = 1.6 |
`∑`pixi2=4.8 |
\[\text{ Mean } = \sum p_i x_i = 1 . 6\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean } \right)^2 \]
\[ = 4 . 8 - 1 . 6^2 \]
\[ = 2 . 24\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance} }\]
\[ = \sqrt{2 . 24}\]
\[ = 1 . 497\]
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