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प्रश्न
Find the variance and standard deviation of the random variable X whose probability distribution is given below :
| x | 0 | 1 | 2 | 3 |
| P(X = x) | `1/8` | `3/8` | `3/8` | `1/8` |
उत्तर
| `x_i` | `p_i` | `p_ix_i` | `p_ix_i^2` |
| 0 | 1/8 | 0 | 0 |
| 1 | 3/8 | 3/8 | 3/8 |
| 2 | 3/8 | 6/8 | 12/8 |
| 3 | 1/8 | 3/8 | 9/8 |
| Total | 12/8 | 24/8 = 3 |
`E(X) = mu = sump_ix_i = 12/8 = 3/2`
`Var(X) = sum_(i=1)^n p_ix_i^2 - mu^2`
`= 3 - (3/2)^2`
`=3 - 9/4`
`= 3/4`
`∴ Var(X) = sigma^2 = 3/4`
Standard deivation of (X) = `sigma_x = sqrt(3/4) =sqrt3/2`
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