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

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.