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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

Consider the Population Described by the Probability Distribution Below x024p(x)131313\begin{array} { c | c | c | c } x & 0 & 2 & 4 \\\hline p ( x ) & \frac { 1 } { 3 } & \frac { 1 } { 3 } & \frac { 1 } { 3 }\end{array}xp(x)​031​​231​​431​​​

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