N-4

1. Closing price data are available from several sources, including **finance.yahoo.com**.

2. Color popularity for 2012 from the Dupont Automotive Color report; see **dupont.com/Media_Center/en_US/color_popularity/2012_assets.html**.

3. The full 2013 Canadian Medical Association report, 13th Annual National Report Card on Health Care, **cma.ca**.

4. Association of Certified Fraud Examiners, Report to the Nations on Occupational Fraud and Abuse 2014, **acfe.com**.

5. U.S. Department of Energy, Annual Energy Review 2011, see **eia.gov/totalenergy/data/annual**.

6. Results from 2011 survey by the Society for Human Resource Management; see **shrm.org**.

7. Results from 2013 study by Jude M. Werra & Associates, see **judewerra.com/liars-index-.html**.

8. 2013 Toronto Resident Casino Survey, conducted by Environics Research Group, **toronto.ca**.

9. The Gallup Organization, *Confidence in Institutions*, June 2013, **gallup.com**.

10. Based on 2011 census data from the website of Statistics Canada; see **statcan.gc.ca**.

11. Harris Poll, “*Cyberchondriacs” on the Rise?*, August 4, 2010, **harrisinteractive.com**.

12. Internet usage statistics, **internetlivestats.com/internet-users**.

13. Canadian transportation statistics from Statistics Canada, **statcan.gc.ca**. U.S. transportation statistics from U.S. Bureau of Transportation Statistics, **bts.gov**.

14. See Note 2.

15. From the website of the Bureau of Labor Statistics, **bls.gov**.

16. M. Ozanian, “The most valuable NFL teams.” From the SportsMoney section of *Forbes* online, **forbes.com/sportsmoney**, August 14, 2013.

17. Estimated probabilities from the National Collegiate Athletic Association (NCAA); see **ncaa.org**. *Note:* The NCAA reports that 1.6% of college seniors are drafted into the NFL. Our use of 1.2% accounts for the attrition of some college players who never make it to their senior year.

N-5

18. See Note 17.

19. W. D. Witnauer, R. G. Rogers, and J. M. Saint Onge, “Major league baseball career length in the 20th Century,” *Population Research and Policy Review* 26 (2007), pp. 371–386.

20. From the Fitch Ratings Global Corporate Finance 2013 Transition and Default Study, **fitchratings.com**.

21. From IRS Tax Statistics; see **irs.gov/uac/Tax-Stats-2**.

22. We use both for the random variable, which takes different values in repeated sampling, and for the numerical value of the random variable in a particular sample. Similarly, stands both for a random variable and for a specific value. This notation is mathematically imprecise but statistically convenient.

23. Based on L. Alwan, M. Xu, D. Yao, and X. Yue, “The Dynamic Newsvendor Model with Correlated Demand,” (January 9, 2015), available online at Social Science Research Network, **ssrn.com/abstract=2547424**.

24. The mean of a continuous random variable with density function can be found by integration:

This integral is a kind of weighted average, analogous to the discrete-case mean

The variance of a continuous random variable is the average squared deviation of the values of from their mean, found by the integral

25. See A. Tversky and D. Kahneman, “Belief in the law of small numbers,” *Psychological Bulletin* 76 (1971), pp. 105–110; and other writings of these authors for a full account of our misperception of randomness.

26. Probabilities involving runs can be quite difficult to compute. That the probability of a run of three or more heads in 10 independent tosses of a fair coin is can be found by clever counting, as can the other results given in the text. A general treatment using advanced methods appears in Section XIII.7 of William Feller, *An Introduction to Probability Theory and Its Applications*, Vol. 1, 3rd ed., Wiley, 1968.

27. R. Vallone and A. Tversky, “The hot hand in basketball: On the misperception of random sequences,” *Cognitive Psychology* 17 (1985), pp. 295–314. A later series of articles that debate the independence question is A. Tversky and T. Gilovich, “The cold facts about the ‘hot hand’ in basketball,” *Chance* 2, no. 1 (1989), pp. 16–21; P. D. Larkey, R. A. Smith, and J. B. Kadane, “It’s OK to believe in the ‘hot hand,"’ *Chance* 2, no. 4 (1989), pp. 22–30; and A. Tversky and T. Gilovich, “The ‘hot hand’: Statistical reality or cognitive illusion?” *Chance* 2, no. 4 (1989), pp. 31–34.

28. As an example, the Charles Schwab’s website (**www.schwab.com**) provides mean returns and standard deviations of returns for all its managed mutual funds under Investment Help.

29. See Note 1.

30. See Note 1.

31. From the 2012 *Statistical Abstract of the United States*, Table 299.

32. Ibid., Table 278.