## 2017-06-14

### Sets, Counting, and Probability (Fall 2005) by Paul G. Bamberg (Harvard Extension School)

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source: It's so blatant    2013年9月13日
This online math course (Math E-102) given by Paul G. Bamberg (Senior Lecturer on Mathematics, Harvard University) develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life. Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas. View complete course (Outline, Problem sets,etc) at: http://www.extension.harvard.edu/open-learning-initiative...

Lec 1 |  1:58:41 Probability, Intuition, and Axioms
- Probability by Symmetry; Probability by Experiment; Payoffs and Probability; Fair Price and Probability; Notation to Combine Sets; Venn Diagrams; Events and Sample Spaces; Event Spaces; Addition of Probabilities; Probability Functions; Inclusion-Exclusion Rule; Many Ways to Skin a Cat
Lec 2 | Sets, Counting, and Probability 1:55:13 Probability by Counting and Inclusion-Exclusion
- Review of the Basics; DeMorgan's Laws; Inclusion-Exclusion; Cups and Saucers; Cups and Saucers # 2; Urns; Family Planning; Twenty-first-Century Sheherezade; Craps; Achilles Rolls of a 6
Lec 3 | 1:51:03 Principles of Counting
- Count A Cartesian Product; The Binomial Theorem; Counting Poker Hands; Counting Bridge Hands; The Munchkin Problem; Genoese Lottery; Counting Suit Patterns; Negative Binomial Theorem; Count by Inclusion-Exclusion
Lec 4 |  1:47:48 Conditional Probability
- St. Paul at Lystra; Conditional Four Aces; Conditional Probability; Independence of Events; Complimentary Events; The Bearded Man Problem; Lemons; Two Useful Theorems; Conditional Munchkins; Monty Hall Problem; Random Desserts
Lec 5 | 59:10 Conditional Craps
- Independence of 3 Events; Compound Experiments; Accidental Independence; Sudden Death; Sampling Paradox
Lec 6 | 1:52:23 Lying Witnesses and Simpson's Paradox
- Wisdom of Solomon; Eddington's Controversy; Affirmative Action; Simpson's Paradox
Lec 7 |  2:00:55 Random Variables
- Discrete Random Variables; Event Space for a DRV; Bridge and Poker; Binomial Distribution; Geometric Distribution; Negative Binomial Distribution; Exponential Function; Poisson Distribution; Distribution Function; Distribution Examples; Function of Random Var; First Computer Project
Lec 8 | 2:00:07 Expectation I
- Unconscious Statistician; Properties of Expectation; Binomial Expectation; Tail-Sum Theorem; Geometric Tail-Sum; Negative Binomial Expectation; Coupons Problem; Variance; Telescoping Series; Convergence
Lec 9 | 1:57:59 Expectation II
- Infinite Expectation; Royal Oak Lottery; Poisson as Limit; Conditional Random Var; Conditional Expectation; Runs of Heads and Tails; Two Wins Takes All
Lec 10 | 1:02:32 Tartan Dice; Terminated Geometric; World Series Pitchers; Negative Hypergeometric; Coin Tossing
Lec 11 | 1:59:17 Gambling
-Casino Night; Random Walk Examples; Random Walk Terminology; Gambler's Ruin; Ruin in Fair Casino; Time until Win or Ruin; A Fair Game; Walk as a Random Variable; Ballot Theorem; Hitting Time Theorem; Expected Lead Times
Lec 12 |  1:53:03 Expected Lead Time; Bijections between Paths
-Another Bijection; Last Visit to Origin; First Visit to Final; First Visit to Max; First Return; Returning Just Once; Strange but True
Lec 13 | 1:51:19 Variables
-First Visit to Max; Sojourn Times; Independent Variables; Uncorrelated Variables: A Counterexample; Generating Function; Product of Gen Functions; A Simple Example; Gen Function for 2 Dice; Clever Loaded Dice; Well-Known Distributions
Lec 14 | 1:54:09 Inequality
-Basic Inequality; Markov's Inequality; Chebyshov's Inequality; Weak Law of Large Numbers; Weak Law, continued; Strong Law of Large Numbers
Lec 15 |  1:26:50 Questions #1--10