Normal sample theorem
Theorem taught in Statistical inference, part of Statistical inference
Normal sample theorem
| Type | Theorem |
| Taught in | Statistical inference |
| Part | Statistical inference |
If X_1,\ldots,X_n are a random sample from \operatorname{N}(\mu,\sigma^2), then
- \overline X is \operatorname{N}(\mu,\sigma^2/n),
- (n-1)s^2/\sigma^2 is \chi^2_{n-1}, and
- \overline X and s^2 are independent.
Used in
- Taught in Statistical inference, where the derivation and examples are.
- Also used in Confidence intervals · Analysis of variance
- All 4 questions on Statistical inference
See also
Random sample · Statistic · Moments of the sample mean and variance · Chi-squared distribution · Student t distribution · F distribution