**A.1. Proof of the basic formulae of statistical inference**

$$\begin{array}{l} E(\infty) = E[(\infty \mathbb{1}, +\infty \mathbb{2} + \dots + \infty n)/n] \\ = [E(\infty \mathbb{1}) + E(\infty \mathbb{2}) + \dots + E(\infty n)]/n \\ = \mu, \text{ since } E(\infty) = \mu \text{ for all } i. \end{array}$$

*Variance(x ) = [var(x1) + var(x2)) + ... + var(xn)]/ n² =[nσ²]/ n²? = σ²/ n Therefore Standard error of x is: SE(x ) = to σ /* √*n*
