The Probability Distribution Shown Below Describes a Population of Measurements $\begin{array}{c|cccc}\hline x & 5 & 9 & 13 & 17 \\\hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\\hline\end{array}$

The probability distribution shown below describes a population of measurements that can assume values of 5, 9, 13, and 17, each of which occurs with the same frequency:

$\begin{array}{c|cccc}\hline x & 5 & 9 & 13 & 17 \\\hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\\hline\end{array}$

Find $E ( x ) = \mu$ . Then consider taking samples of $n = 2$ measurements and calculating $\bar { x }$ for each sample. Find the expected value, $E ( \bar { x } )$ , of $\bar { x }$ .