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

question 7

Essay

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?