The Probability Distribution Shown Below Describes a Population of Measurements $\begin{array}{c|cccc}\hline x & 5 & 9 & 13 & 17 \\\hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\\hline\end{array}$

question 35

Essay

The probability distribution shown below describes a population of measurements that can assume values of 5, 9, 13, and 17, each of which occurs with the same frequency:

$\begin{array}{c|cccc}\hline x & 5 & 9 & 13 & 17 \\\hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\\hline\end{array}$

Find $E ( x ) = \mu$ . Then consider taking samples of $n = 2$ measurements and calculating $\bar { x }$ for each sample. Find the expected value, $E ( \bar { x } )$ , of $\bar { x }$ .

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Definitions:

Thermoregulatory Center

The part of the brain that regulates body temperature, located in the hypothalamus.

Sensory Receptors

Specialized cells or nerve endings that respond to changes in the environment by converting energy from stimuli into nerve impulses.

Hollow Interior

Refers to the inner empty space or cavity within an organ or structure.

Filter Blood

The process of removing waste products and excess substances from the bloodstream, primarily performed by the kidneys.