The Random Variable X Has the Following Probability Distribution $$\begin{array} { c c } x &fx) \\0 & .25 \\1 & .20 \\2 & .15 \\3 & .30 \\4 & .10\end{array}$$

Short Answer

The random variable x has the following probability distribution:
$$\begin{array} { c c } x &fx) \\0 & .25 \\1 & .20 \\2 & .15 \\3 & .30 \\4 & .10\end{array}$$
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.