AP Statistics 2016-2017

Chapter 7: Random Variables

7.1: Discrete and Continuous Random Variables

7.2: Means and Variances of Random Variables

"I was gratified to be able to answer promptly. I said I don't know."
-- (Mark Twain)

The Pythagoreans (cult whose leader was Pythagoras, founded around 500 B.C.) were number mystics, not scientific sages. Long after the death of Pythagoras, the cult split into two distinct schools. Those who continued with mysticism and rituals became the akousmatikoi (translated "those who hear") school. The other school drifted away from the mystic approach to numbers and used them for what we would call scientific purposes. This group represented the mathematikoi (translated "those interested in science") school. Do you see where our modern word mathematics comes from?

Assignment # 1 (Introduction & §7.1)Th:[11-17-16]

Read pp. 388 – 395. Take notes on all terminology.

pp. 395 – 397 # 7.1 – 7.5

Assignment # 2 (Introduction & §7.1)F:[11-18-16]

Read pp. 397 – 401. Take notes on all terminology.

pp. 401 – 402 # 7.6 – 7.9

Assignment # 3 (§7.2)M:[11-21-16]

Read pp. 407 – 411. Take notes on all terminology.

pp. 411 – 413 # 7.22 – 7.29

Assignment # 4 (§7.2)T:[11-22-16]

Read pp. 413 – 416; pp. 418 – 425. Take notes on all terminology.

pp. 416 – 418 # 7.30 – 7.33; pp. 425 – 426 # 7.34 – 7.41

Assignment # 5 (§7.1 Review) M:[11-28-16]

Read pp. 402 – 403. Take notes on all terminology.

pp. 403 – 407 # 7.10 – 7.21

Assignment # 6 (§7.2 Review)T:[11-29-16]

Read pp. 426 – 427

pp. 427 – 430 # 7.42 – 7.53

Assignment # 7 (§7.1-7.2 Review) W:[11-30-16]

Read pp. 430 – 431.

pp. 431 – 435 # 7.54 – 7.68

Assignment # 8 (§7.1-7.2 Review) Th:[12-01-16]

Take-home Quiz Practice Test TBA

Assignment # 9 (§7.1-7.2 Review) F:[12-02-16]

Take-home Quiz Practice Test TBA

Assignment # 10 (§7.1-7.2 Test) M:[12-05-16]

Key Words, Skills, Terminology and Concepts

Random Variable / Discrete Random Variable / Probability Distribution / Probability Histogram / Continuous Random Variable
Density Function/Curve / Uniform Distribution / Probability of an Individual Outcome / Normal Distribution / Mean of a Random Variable
Expected Value / Variance of a Random Variable / Law of Large Numbers / Law of Small Numbers / Rules for Menas
Rules for Variances

Usage of the TI-83 –MATH PRB 6:randNorm (mean, std. dev., sample size);
2nd LIST OPS 5:seq( X, X, begin #, end #)

"Obvious is the most dangerous word in mathematics."
-- (Eric TempleBell )

PAPPUS (ca 300): An excellent mathematician who lived in Alexandria, Pappus attempted to rekindle interest in the mathematical works of the Greeks. This was not an easy task, since Christians had destroyed much of the ancient Greek documents, but Pappus managed to create his Mathematical Collection which cites or references over thirty different ancient mathematicians. Much of our knowledge of Greek mathematics has been derived from the works of Pappus.

"There are no facts, only interpretations."
-- (Frederick Nietzsche )

The ancient Greeks were masters of geometry, but they shied away from the concept of the infinite. No one was more influential in promoting a suspicion of the infinite than Zeno of Elea (ca 450 B.C.). Zeno produced mathematical paradoxes that seemed to prove that motion is impossible and that certain frequently observed events can't happen. Try as they might, the Greeks could not resolve Zeno's paradoxes, the most famous of which is The Achilles. Zeno "proved" that Achilles could not beat a tortoise in a race if the tortoise had a head start and continued to move, no matter how slowly.

For 2000 years, the concept of infinity puzzled even the greatest of mathematicians. It was Georg Cantor (1845- 1918) who finally resolved the mysteries of the infinite.

"A winner says, 'It may be difficult, but it's possible.'
A loser says, 'It may be possible, but it's too difficult.' "
-- (Dr. Robert Anthony, Betting on Yourself )

HYPATIA (370 - 415): First "known" female mathematician. Like her father, Theon of Alexandria, Hypatia was a Pythagorean, a Platonist, and a pagan. She was an outstanding mathematician and teacher during a time when women were not supposed to exercise such qualities. She was brutally murdered by Christian zealots. Do some research and learn about why Hypatia finds a place in the history of mathematics.