Consider the Given Discrete Probability Distribution $\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 \\\hline p(x) & .1 & .2 & .2 & .3 & .2 \\\hline\end{array}$

question 49

Essay

Consider the given discrete probability distribution. $\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 \\\hline p(x) & .1 & .2 & .2 & .3 & .2 \\\hline\end{array}$

a. Find $\mu = E ( x )$ .
b. Find $\sigma = \sqrt { E \left[ ( x - \mu ) ^ { 2 } \right] }$ .
c. Find the probability that the value of $x$ falls within one standard deviation of the mean. Compare this result to the Empirical Rule.

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Definitions:

Hydrochloric Acid

A strong, corrosive acid that is a component of gastric juice in the stomach, aiding in digestion and sterilizing ingested food.

Acidic

Having a pH less than 7, typically described for solutions that have a higher concentration of hydrogen ions.

Given Element

A chemical element specified or identified in a particular context or situation.

Protons Only

Describes an atomic composition focusing solely on protons, the positively charged particles in an atom's nucleus, ignoring other particles.