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

Essay

The probability distribution shown below describes a population of measurements that
can assume values of 1, 5, 9, and 13, each of which occurs with the same frequency: $\begin{array}{l|cccc}\hline x & 1 & 5 & 9 & 13 \\\hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\\hline\end{array}$

Consider taking samples of $n = 2$ measurements and calculating $\bar { x }$ for each sample. Construct the probability histogram for the sampling distribution of $\bar { x }$ .