Consider the Probability Distribution Shown Here $\begin{array}{l|rrr}\hline x & 0 & 2 & 4 \\\hline p(x) & \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\\hline\end{array}$

Essay

Consider the probability distribution shown here.

$\begin{array}{l|rrr}\hline x & 0 & 2 & 4 \\\hline p(x) & \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\\hline\end{array}$

Let $\bar { x }$ be the sample mean for random samples of $n = 2$ measurements from this distribution. Find $E ( x )$ and $E ( \bar { x } )$ .