Category:Central Limit Theorem

This category contains pages concerning Central Limit Theorem:

Let $X_1, X_2, \ldots$ be a sequence of independent identically distributed real-valued random variables with:

expectation $\expect {X_i} = \mu \in \R$

variance $\var {X_i} = \sigma^2 > 0$

Let:

$\ds S_n = \sum_{i \mathop = 1}^n X_i$

Then:

$\dfrac {S_n - n \mu} {\sqrt {n \sigma^2} } \xrightarrow D \Gaussian 0 1$ as $n \to \infty$

that is, converges in distribution to a standard Gaussian.