Average Calculation

Let V₁,...,V_n be independent identical distributed (i.i.d) random variables.
We assume $\vert V_{i}\vert \leq M$.
The average can be written as :

$\hat{V_{N}} = \frac{1}{N}\sum_{i=1}^{N}V_{i}$

or as a recursive online formula :

$\hat{V_{k}} = (1-\frac{1}{k}) \hat{V}_{k-1} +\frac{1}{k}V_{k}$
(Since: $(1-\frac{1}{k})\hat{V}_{k-1}= \frac{k-1}{k}(\frac{1}{k- 1}\sum_{i=1}^{k-1}V_{i})$ )