State Whether or Not Each of the Following Are Valid $\begin{array}{c|cccc}x & 0 & 1 & 2 & 3 \\\hline p(x) & .15 & .25 & .35 & .45\end{array}$

question 49

Essay

State whether or not each of the following are valid probability distributions, and if not, explain why not. a.
$\begin{array}{c|cccc}x & 0 & 1 & 2 & 3 \\\hline p(x) & .15 & .25 & .35 & .45\end{array}$

b.
$\begin{array}{c|cccc}x & 2 & 3 & 4 & 5 \\\hline p(x) & -.10 & .40 & .50 & .25\end{array}$

c.
$\begin{array}{c|ccccc}x & -2 & -1 & 0 & 1 & 2 \\\hline p(x) & .10 & .20 & .40 & .20 & .10\end{array}$

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Definitions:

Normal Distributions

Symmetrical bell-shaped distributions that describe how data points are dispersed or spread out across the mean.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values, indicating how much the values differ from the mean.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values, showing how much each value differs from the mean.

Normal Distribution

A bell-shaped curve which describes the spread of a characteristic throughout a population, where most occurrences take place around the central peak and probabilities for values taper off equally towards both tails.