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 μ. 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 μ 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 μ? Why? 6.3 The Sampling Distribution of x-bar and the Central Limit Theorem 1 Understand Central Limit Theorem