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

question 24

Essay

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 $\sigma ^ { 2 }$ .

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Definitions:

Middle Three Quintiles

The segments of the population that fall into the second, third, and fourth quintiles when dividing the total population into five equal groups based on income or wealth.

Income Received

It refers to the total amount of money obtained by individuals or entities typically through employment, investments, or other sources.

Upper Quintiles

Refers to the top 20% of a population in terms of income or wealth distribution.

Line L

Represents the relationship between the quantity of labor hired and the amount of output produced, often used in economics to illustrate productivity.