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

question 58

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.

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Definitions:

Preferred Dividends

Payments made to preferred shareholders before common shareholders receive any dividends.

After-Tax Income

The net income an individual or corporation receives after all income taxes have been deducted from gross income.

Common Shareholders

Individuals or entities that own common shares in a corporation, granting them voting rights and a share in the company’s profits via dividends.

EPS

Earnings Per Share; a company's profit divided by the outstanding shares of its common stock.