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 $\sigma ^ { 2 }$.
b. Find the sampling distribution of the sample variance $s ^ { 2 }$ for a random sample of $n = 2$ measurements from the distribution.
c. Show that $s ^ { 2 }$ is an unbiased estimator of $\sigma ^ { 2 }$.

Question

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 $\sigma ^ { 2 }$.
b. Find the sampling distribution of the sample variance $s ^ { 2 }$ for a random sample of $n = 2$ measurements from the distribution.
c. Show that $s ^ { 2 }$ is an unbiased estimator of $\sigma ^ { 2 }$.

Quizplus · Accepted Answer

The Answer of 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 $\sigma ^ { 2 }$.
b. Find the sampling distribution of the sample variance $s ^ { 2 }$ for a random sample of $n = 2$ measurements from the distribution.
c. Show that $s ^ { 2 }$ is an unbiased estimator of $\sigma ^ { 2 }$.

Consider the Population Described by the Probability Distribution Below x357p(x).1.7.2\begin{array}{c|c|c|c}x & 3 & 5 & 7 \\\hline p(x) & .1 & .7 & .2\end{array}xp(x)​3.1​5.7​7.2​​

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