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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

Consider the Given Discrete Probability Distribution x12345p(x).1.2.2.3.2\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}xp(x)​1.1​2.2​3.2​4.3​5.2​​

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