combinatorics

First moment Population: $ \Omega = \{ x_1, \dots, x_N \} $ Collection of $n$-samples: $\mathcal{S} = \{ s \in \Omega^n \mid \forall i,j \in s, i \ne j \} $ Collection of $n$-samples containing $x$: $ \mathcal{S}_x = \{ s \in \mathcal{S} \mid x \in s \} $ Observe that $ |\mathcal{S}_x| = \binom{N-1}{n-1} $. Let population mean be zero. $\mu = 0$, i.e. $ \sum_{i = 1}^N x_i = 0 $ [Read More]