The Probability Distribution Shown Below Describes a Population of Measurements $\begin{array}{l|cccc}\hline x & 5 & 10 & 15 & 20 \\\hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\\hline\end{array}$

Essay

The probability distribution shown below describes a population of measurements that
can assume values of 5, 10, 15, and 20, each of which occurs with the same frequency: $\begin{array}{l|cccc}\hline x & 5 & 10 & 15 & 20 \\\hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\\hline\end{array}$

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 $\bar { x }$ .