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

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