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 36

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:

MC

Short for Marginal Cost, it refers to the additional cost incurred by producing one more unit of a product or service.

Total Revenue

The total income generated by a firm from the sale of its goods and services, calculated as the selling price per unit times the number of units sold.

Variable Costs

Costs that change in proportion to the level of activity or production volume, such as materials and direct labor.

Average Total Cost

The sum of all production costs (both fixed and variable) divided by the total amount of goods produced.