Read the book "The Drunkard's Walk - How Randomness Rules Our Lives" by Mlodinow and pay special attend to the following questions. Some of these questions may appear on quizzes and exams.
Chapter 1 Peering through the Eyepiece of Randomness
1. Explain the phenomenon "regression toward the mean."
In any series of random events an extraordinary event is most likely to be followed, due purely to chance, by a more ordinary one.
2. What factors determine whether a person will be successful in career, investment, etc.?
Success in our careers, in our investments, and in our life decisions, both major and minor—is as much the result of random factors as the result of skill, preparedness, and hard work.
3. Was Paramount's
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Since the company has no data on you—no idea of the “position of the first ball”—it might assign you an equal prior probability of being in either group, or it might use what it knows about the general population of new drivers and start you off by guessing that the chances you are a high risk are, say, 1 in 3. In that case the company would model you as a hybrid—one-third high risk and two-thirds low risk—and charge you one-third the price it charges high-risk drivers plus two-thirds the price it charges low risk drivers. Then, after a year of observation—that is, after one of Bayes’s second balls has been thrown—the company can employ the new datum to reevaluate its model, adjust the one-third and two-third proportions it previously assigned, and recalculate what it ought to charge. If you have had no accidents, the proportion of low risk and low price it assigns you will increase; if you have had two accidents, it will decrease. The precise size of the adjustment is given by Bayes’s theory. In the same manner the insurance company can periodically adjust its assessments in later years to reflect the fact that you were accident-free or that you twice had an accident while driving the wrong way down a one way street, holding a cell phone with your left hand and a doughnut with your right. That is why insurance companies can give out “good driver” discounts: the absence of accidents