Statistikk og Simulering

# Økt 13. Estimation of the Mean

## The sample mean

#### 14.2. The sample mean

Let ${X}_{1},{X}_{2},\dots ,{X}_{n}$ be independent stochastic variables, the we have TODO

Tabell 1: Two important formulæ, repeated from Session 2.

The sample mean $\stackrel{̄}{X}$ is a stochastic variable. Considering a single observation of $X$, the expected value is $E\left(X\right)=\mu$ and the variance is $var\left(X\right)={\sigma }^{2}$.

Øving 14.2 Write down the formulæ for $\stackrel{̄}{X}$ in terms of a $n$ observations ${X}_{1},{X}_{2},\dots ,{X}_{n}$.

Øving 14.3 Give formulæ for $E\left(\stackrel{̄}{X}\right)$ and $var\left(\stackrel{̄}{X}\right)$.