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प्रश्न
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -2 | -1 | 0 | 1 | 2 |
| pi : | 0.1 | 0.2 | 0.4 | 0.2 | 0.1 |
उत्तर
| xi | pi | pixi | `∑`pixi2 |
| -2 | 0.1 | -0.2 | 0.4
|
| -1 | 0.2 | -0.2 | 0.2 |
| 0 | 0.4 | 0 | 0 |
| 1 | 0.2 | 0.2 | 0.2 |
| 2 | 0.1 | 0.2 | 0.4 |
| `∑`pixi = 0 | `∑`pixi2 = 1.2
|
\[\text{ Mean } = \sum p_i x_i = 0\]
\[\text{ Variance } = \sum p_i {x_i}2^{}_{} - \left( \text{ Mean} \right)^2 \]
\[ = 1 . 2 - 0^2 \]
\[ = 1 . 2\]
\[\text{ Step Deviation } = \sqrt{\text{ Variance } } \]
\[ = \sqrt{1 . 2}\]
\[ = 1 . 095\]
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Solution:
Here, n = 4
p = probability of defective device = 10% = `10/100 = square`
∴ q = 1 - p = 1 - 0.1 = `square`
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`P(X=x)=""^n"C"_x p^x q^(n-x)= ""^4"C"_x (0.1)^x (0.9)^(4 - x)`
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∴ P[X ≤ 1] = `square`
