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

---

Definitions:

Green Marketing

Marketing efforts focused on promoting products or services based on their environmental benefits, often highlighting sustainability and eco-friendly practices.

Stakeholder Responsibility

The obligations of an organization towards individuals or groups that have a stake in its operations and decisions, including employees, customers, and the community.

Marketing Concept

A business philosophy suggesting that achieving organizational goals depends on knowing the needs and wants of target markets and delivering desired satisfactions better than competitors.

Social Audit

A formal review of a company's initiatives, procedures, and codes of conduct regarding social responsibility, assessing their impact on society.