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**4.1 Randomness****4.2 Probability Models****4.3 General Probability Rules****4.4 Random Variables****4.5 Means and Variances of Random Variables**

In this chapter, we study basic concepts of probability. The first two chapters focussed on exploring and describing data in hand. In Chapter 3, we learned how to produce quality data that can be reliably used to infer conclusions about the wider population.

You might then ask yourself, “Where does the study of probability fit in our data journey?” The answer lies in recognizing that the reasoning of statistical inference rests on asking, “How often would this method give a correct answer if I used it very many times?” When we produce data by random sampling a randomized comparative experiment, the laws of probability answer the question, “What would happen if we repeated this process many times?” As such, *probability* can be viewed as the backbone of statistical inference.

The importance of probability ideas for statistical inference is reason enough to delve into this chapter. However, our study of probability is further motivated by the fact that businesses use probability and related concepts as the basis for decision making in a world full of risk and uncertainty.

- As a business student reading this book, there is a good chance you are pursuing an accounting major with the hope to become a certified public accountant (CPA). Did you know that accountants can boost their earnings potential by additional 10% to 25% by adding a certification for fraud detection? Certified fraud accountants must have in their toolkit a probability distribution that we study in this chapter. Liberty Mutual Insurance, Citibank, MasterCard, Deloitte, and the FBI are just a few of the organizations that employ fraud accountants.
- With shrinking product life cycles, what was a “hot” seller quickly becomes obsolete. Imagine the challenge for Nike in its decision of how many Dallas Cowboys jersey replicas to produce with a certain player's name. If Nike makes too many and the player leaves for another team, Nike and shops selling NFL apparel will absorb considerable losses when stuck with a nearly unsellable product. We will explore how probability can help industries with short product life cycles make better decisions.
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- Financial advisers at wealth management firms such as Wells Fargo, Fidelity Investments, and J.P. Morgan Chase routinely provide advice to their clients on investments. Which ones (stocks, mutual funds, bonds, etc.) should their clients buy? How much in each possible investment should their clients invest? We will learn that their advice is guided by concepts studied in this chapter.
- Online bookseller
**Amazon.com**serves its U.S. customers with inventory consolidated in only a handful of warehouses. Each Amazon warehouse pools demand over a large geographical area, which leads to lower total inventory versus having many smaller warehouses. We will discover the principle as to why this strategy provides Amazon with a competitive edge.