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 31

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:

Limited Population

Refers to a specific, finite group of entities or individuals being studied or served.

Unlimited Queue Length

A scenario in queue theory where there is no limit to the number of entities that can wait in line for service or processing.

Limited Queue Length

In operations management, it refers to a constraint on the maximum number of items or entities that can wait in line to be processed.

Multichannel

Refers to using multiple channels of communication or distribution to interact with customers or deliver products/services.