Moments of the sample mean and variance
Proposition taught in Statistical inference, part of Statistical inference
Moments of the sample mean and variance
| Type | Proposition |
| Taught in | Statistical inference |
| Part | Statistical inference |
If X_1,\ldots,X_n are a random sample from a distribution with mean \mu and variance \sigma^2, then
\mathbb{E}\overline X=\mu,\qquad \operatorname{Var}(\overline X)=\frac{\sigma^2}{n},\qquad \mathbb{E} s^2=\sigma^2.
No normality is needed.
Used in
- Taught in Statistical inference, where the derivation and examples are.
- All 4 questions on Statistical inference
See also
Random sample · Statistic · Chi-squared distribution · Student t distribution · F distribution · Normal sample theorem