"Angling may be said to be so like mathematics that it cannot fully be learned." -- (The Complete Angler, 1653) Trigonometry: An amazing number of useful relationships come from the three simple definitions for sine, cosine, and tangent. The Muslims introduced these ratios and established many of the extremely important trigonometric relationships that we use today. Muslim developers of trigonometry include Al-Battani (ca. 920) Abu Wafa (ca. 980) Ibn Yunus (ca. 1000) Thabit ibn Qurra (ca. 900) Nasir al-Din al-Tusi (ca. 1260) Why did Herkimer cut a hole in the carpet at a Las Vegas nightclub? Answer: So he could see the floor show. Things Herky would like to know: Some folks seem to be luckier than others. Why does an orthopedist get all the breaks? Is it OK to get angry with a dermatologist who makes rash statements? ASSIGNMENT #51 Reading: Section 8.2 Summary (Link from this page) Exercises: 8.37, 8.38, 8.39, 8.40 (starting on page 447). NOTE: In exercise 8.40, you don't have to worry about the Minitab explanation. Just understand the tables on page 449 and answer the questions using them. You are working with ideas and concepts fromChapter 8.

Note: The only reference to the geometric distribution on the APSyllabus appears in Section III (A,4). This reads "Simulation of probability distributions, includingbinomial and geometric." No geometricdistribution formulas appear on the AP Formula Sheet that studentshave available when they take the AP exam.

Here are two examples contrasting binomial and geometric settings. Note thedifferent definitions of the variable x.

BINOMIAL SETTING:

A fair die is rolled twenty times. Let x = the number of 6's obtained. Possible values for x are in theset {0,1,2,...,18,19,20} and mx = Np = 20(1/6) = 3.3333

GEOMETRIC SETTING:

A fair die is rolled until a 6appears. Let x = the number of rolls required to get a 6. There area countless number of values for x, which is a member of the set ofpositive integers. In this situation, mx = 1/p = 1/(1/6) = 6. (See explanation in Section 8.2Summary.)

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Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)