Central Limit Theorem (Edexcel A-Level Further Mathematics): Flashcards

$\bar{X} \sim N(\mu, \frac{\sigma^2}{n})$

Exact for normal populations; approximate for non-normal with large n

$n \geq 25$

For non-normal or unknown distributions with large n

$\frac{\sigma^2}{n}$

Use $s^2$ (sample variance)

$E(Y) = \sum y \cdot P(Y=y)$

$E(Y^2) = \sum y^2 \cdot P(Y=y)$

$\text{Var}(Y) = E(Y^2) - [E(Y)]^2$

$\frac{1}{n}$