"Algebra is the intellectual instrument for rendering clear the quantitative aspects of the world." -- (Alfred North Whitehead, 1861-1947)
Galileo Galilei (1564-1642): He was the first to seek mathematical formulas to describe falling bodies. Like Copernicus, Galileo was convinced that the earth was not the center of the universe. Because his discoveries roused church opposition, Galileo was summoned to appear before the Inquisition. He had to make life-saving confessions, and "officially deny" his scientific findings. In 1992, Pope John Paul II officially stated that the Roman Catholic Church erred in condemning Galileo 359 years earlier.
How did Herkimer keep a herd of elephants from charging?
Answer: He took away their credit cards.
Things Herky would like to know:
If the early bird gets the worm, why does the second mouse always get the cheese in the trap?
If you shouldn't sweat petty things, should you be allowed to pet sweaty things?
Reading: Section 6.1 (pages 310-316).
Exercises: Do Test 5A (Handout in class).
You are reading in Section 6.1 and working onproblems (Test 5A) from Chapter 5.
Key words in this section include
Independence is avery important concept in probability. Two events are independent ifthe outcome of one event does not influence the outcome of the secondevent. For instance, let E1 be the event "randomly picking a studentfrom the AP Statistics class to answer a question," and E2 be theevent "randomly picking a student from the AP Statistics class toanswer a second question.? Are E1 and E2 independent events?
Answer: The response depends onwhether the first student is "replaced" before randomly choosing astudent to answer the second question. If the sampling is donewith replacement,
then E1 and E2 are independent. For instance, if the classhas 10 students, and if Herkimer is one of the students, then theprobability he is chosen to answer the second question is 1/10. Ifthe sampling is done withoutreplacement, then the probability ofHerkimer being chosen to answer the second question is either 0 (ifhe was randomly chosen to answer the first question) or 1/9 (if hewas not randomly chosen to answer the first question.). In thissituation, the outcome of E2 is clearly dependent upon the outcome ofE1.
LINK TO SECTIONSUMMARIES
LINK TO STATISTICS HOMEPAGE
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)
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)
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