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

question 3

Essay

State whether or not each of the following are valid probability distributions, and if not, explain why not.
a. $\begin{array} { c | c c c c } x & 0 & 1 & 2 & 3 \\\hline p ( x ) & .15 & .25 & .35 & .45\end{array}$
b. $\begin{array} { c | c c c c } x & 2 & 3 & 4 & 5 \\\hline p ( x ) & - .10 & .40 & .50 & .25\end{array}$
c. $\begin{array} { c | c c c c c } x & - 2 & - 1 & 0 & 1 & 2 \\\hline p ( x ) & .10 & .20 & .40 & .20 & .10\end{array}$

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Definitions:

Tholos

A circular building of ancient Greek and Roman architecture, typically set at a sanctuary, characterized by a conical or dome-shaped roof.

Pylon

The wide entrance gateway of an Egyptian temple, characterized by its sloping walls.

Androgynous

Exhibiting characteristics or qualities of both male and female.

Akhenaton

An ancient Egyptian pharaoh of the 18th dynasty who is noted for abandoning traditional Egyptian polytheism and introducing worship centered around Aten.