Consider the Population Described by the Probability Distribution Below $\begin{array}{c|c|c|c}x & 0 & 2 & 4 \\\hline p(x) & \frac{1}{3} & \frac{1}{3} & \frac{1}{3}\end{array}$

Consider the population described by the probability distribution below. $\begin{array}{c|c|c|c}x & 0 & 2 & 4 \\\hline p(x) & \frac{1}{3} & \frac{1}{3} & \frac{1}{3}\end{array}$

a. Find $\mu$ .
b. Find the sampling distribution of the sample mean for a random sample of $n = 3$ measurements from this distribution. c. Find the sampling distribution of the sample median for a random sample of $n = 3$ observations from this population.
d. Show that both the mean and the median are unbiased estimators of $\mu$ for this population.
e. Find the variances of the sampling distributions of the sample mean and the sample median.
f. Which estimator would you use to estimate $\mu$ ? Why?