The Probability Distribution Shown Below Describes a Population of Measurements $$\begin{array} { c | c c c } \mathrm { x } & 0 & 2 & 4 \\\hline \mathrm { p } ( \mathrm { x } ) & 1 / 3 & 1 / 3 & 1 / 3\end{array}$$

The probability distribution shown below describes a population of measurements. $$\begin{array} { c | c c c } \mathrm { x } & 0 & 2 & 4 \\\hline \mathrm { p } ( \mathrm { x } ) & 1 / 3 & 1 / 3 & 1 / 3\end{array}$$ Suppose that we took repeated random samples of n = 2 observations from the population described above. Which of the following would represent the sampling distribution of the sample mean? A) $\begin{array}{c|ccc}\bar{x} & 0 & 2 & 4 \\\hline\mathrm{p}(\bar{x})& 1 / 3 & 1 / 3 & 1 / 3\end{array}$

B) $\begin{array}{c|ccccc}\bar{x} & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm{p}(\bar{x}) & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5\end{array}$

C) $\begin{array}{c|ccccc}\overline{\mathrm{x}} & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm{p}(\overline{\mathrm{x}}) & 2 / 9 & 2 / 9 & 1 / 9 & 2 / 9 & 2 / 9\end{array}$

D) $\begin{array}{c|ccccc}\overline{\mathrm{x}} & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm{p}(\overline{\mathrm{x}}) & 1 / 9 & 2 / 9 & 3 / 9 & 2 / 9 & 1 / 9\end{array}$