# Math 20: Discrete Probability

Last updated November 29, 2010

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# Syllabus

The following is a rough syllabus for the course.

Lectures
Section In Text
Brief Description
9/22 Introduction to Probability ( Heads or Tails Simulation , Coin Tosses Simulation )
X-Hour No X-Hour
9/24 1.2 Basic Set Operations, Random Variables, Sample Spaces
9/27 1.2 Distribution Functions, Coin Toss Experiments, Probability vs. Odds
9/29 3.1 Permutations, Combinations, Birthday Problem ( Birthday Problem Simulation )
X-hour (Optional) Proof-writing Workshop
10/1 3.1 Asymptotic Equality, Stirling's Formula, Distribution of Prime Numbers ( Stirling's Formula Simulation)
10/4 3.2 Binomial Coefficients, Pascal's Triangle, Poker Hands
10/6 3.2 Inclusion-Exclusion, Hat Check Problem
X-Hour Quiz #1: Basic Probability and Combinatorics (sections 1.2, 3.1 in text)
10/8 More Topics In Combinatorics: Bernoulli Trials and ``Stars and Bars''-type Problems
10/11 4.1 Conditional Probability, Monty Hall Problem ( Monty Hall Interactive Feature)
10/13 4.1 Independent Events
X-Hour (Optional) Proof-writing Workshop, part II
10/15 4.1 Bayes Formula, Applications to Medicine and Law ( NY Times Article)
10/18 6.1 Average Value, Expected Value ( Die Simulation)
10/20 6.1 The St. Petersburg Paradox, Properties of Expected Values ( Craps Simulation)
X-Hour No X-Hour
10/22 6.1 Independent Random Variables, Conditional Expectation
10/25 6.2 Variance, Standard Deviation
10/27 5.1 Important Distributions I: Discrete Uniform & Binomial Distributions ( Galton Board Applet )
X-Hour 5.1 Important Distributions II: The Poisson Distribution, Horse-Kick Deaths; Midterm Exam 7 - 9 PM
10/29 No Class - Homecoming!
11/1 5.1 Important Distributions III: Geometric, Negative Binomial & Hypergeometric Distributions; The Benford Distribution
11/3 8.1 The Coupon Collector Problem, Chebyshev's Inequality
X-Hour No X-Hour
11/5 8.1 Law of Large Numbers, Dice-Rolling Experiment
11/8 9.1 Central Limit Theorem: Geometric Motivation
11/10 9.1 Central Limit Theorem: Proof Sketch and Examples
X-Hour Quiz #2: Important Distributions, Law of Large Numbers (sections 5.1, 8.1 in text)
11/12 9.2 Central Limit Theorem: Generalizations, Application to Genetics
11/15 Confidence Intervals and The Embarrassing Question Experiment
11/17 11.1 Introduction to Markov Chains
X-Hour (Optional) Linear Algebra Tutorial
11/19 11.2 Absorbing Markov Chains
11/22 11.3 Regular and Ergodic Markov Chains
11/24 No Class - Thanksgiving Break!
11/29 Markov Chains Applications: Google's PageRank Algorithm, Monopoly( Slides )
12/1 Final Exam Review - Probability Theory Jeopardy!