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Course

Code:	MATH E-102
Subject:	Mathematics
Topic:	Probability
Views:	28,214

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Harvard University

Name:	Harvard University (Harvard)
Type:	University

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Sets, Counting, and Probability

Video Lectures

Displaying all 15 video lectures.

Lecture 1 Play Video	Probability, Intuition, and Axioms Topics: 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
Lecture 2 Play Video	Probability by Counting and Inclusion-Exclusion Topics: 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
Lecture 3 Play Video	Principles of Counting Topics: 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
Lecture 4 Play Video	Conditional Probability Topics: 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 DessertsThese lectures were offered as an online course at the Harvard Extension SchoolThis online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life.View complete course (Outline, Problem sets,etc) at: http://www.extension.harvard.edu/open-learning-initiative/se...
Lecture 5 Play Video	Conditional Craps Topics: Independence of 3 Events; Compound Experiments; Accidental Independence; Sudden Death; Sampling Paradox
Lecture 6 Play Video	Lying Witnesses and Simpson's Paradox Topics: Wisdom of Solomon; Eddington's Controversy; Affirmative Action; Simpson's Paradox
Lecture 7 Play Video	Random Variables & Distributions Topics: 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
Lecture 8 Play Video	Expectation I: Binomial Expectation & Variance Topics: Unconscious Statistician; Properties of Expectation; Binomial Expectation; Tail-Sum Theorem; Geometric Tail-Sum; Negative Binomial Expectation; Coupons Problem; Variance; Telescoping Series; Convergence
Lecture 9 Play Video	Expectation II: Infinite & Conditional Expectation Topics: Infinite Expectation; Royal Oak Lottery; Poisson as Limit; Conditional Random Var; Conditional Expectation; Runs of Heads and Tails; Two Wins Takes All
Lecture 10 Play Video	Geometric & Negative Hypergeometric Distributions Topics: Tartan Dice, Terminated Geometric, World Series Pitchers, Negative Hypergeometric, Coin Tossing
Lecture 11 Play Video	Gambling: Random Walks & Gambler's Ruin Topics: 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
Lecture 12 Play Video	Expected Lead Time & Bijections between Paths Topics: 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
Lecture 13 Play Video	Variables: Independent, Uncorrelated, & Generating Functions Variables-First Visit to Max; Sojourn Times; Independent Variables; Uncorrelated Variables: A Counterexample; Generating Function; Product of Generating Functions; A Simple Example; Generating Function for 2 Dice; Clever Loaded Dice; Well-Known Distributions
Lecture 14 Play Video	Basic Inequality, Markov's Inequality & Chebyshov's Inequality Topics: Basic Inequality; Markov's Inequality; Chebyshov's Inequality; Weak Law of Large Numbers; Weak Law, continued; Strong Law of Large Numbers
Lecture 15 Play Video	Review and Questions #1-10 In the last lecture, Prof. Bamberg concludes the lecture by working on 10 exercises with the class.