Consider the Population Described by the Probability Distribution Below $\begin{array}{c|c|c|c}x & 3 & 5 & 7 \\\hline p(x) & .1 & .7 & .2\end{array}$

Essay

Consider the population described by the probability distribution below. $\begin{array}{c|c|c|c}x & 3 & 5 & 7 \\\hline p(x) & .1 & .7 & .2\end{array}$

a. Find $\mu$ .
b. Find the sampling distribution of the sample median for a random sample of $n = 2$ observations from this population.
c. Show that the median is an unbiased estimator of $\mu$ .