Lectures |
Sections in Text |
Brief Description |
Monday 9/12 |
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Course topic and objectives
Course details: office hours, grades, exams, HW
Teamwork exercise: the Josephus Problem
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Wednesday 9/14 |
1.2 |
Basic concepts and language: experiment, outcome, sample space, probability
distribution, uniform distribution, independent trials, law of large numbers,
event
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Friday 9/16 |
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Multiple event probabilities (union, complement,…)
Random Variable (numerical function on a sample space)
Distribution of a random variable
Odds
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Monday 9/19 |
3.2 |
HW #1 Due
Subsets, binomial coefficient, Pascal’s triangle, binomial theorem
Binomial distribution
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Wednesday 9/21 |
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Riffle shuffling
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Friday 9/23 |
3.1 |
Permutations, factorial, Stirling’s Formula
Principle of Inclusion-Exclusion
Hat Check Problem
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Monday 9/26 |
4.1 |
HW #2 Due
Conditional probability of one event given another
Monty Hall Problem
Independent events, mutually independent set of events
Product formula for probability of intersection of independent events
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Wednesday 9/28 |
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Independent Random Variables
Expectation and variance of a random variable, examples
Expectation linear always, variance additive if independent
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Thursday 9/29 |
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Applications of linearity of expectation
ESP problem
Buffon’s Needle
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Friday 9/30 |
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Bayes’ Formula, examples
Further examples of conditional probability
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Monday 10/3 |
5.1 |
HW #3 Due
Important distributions: Descriptions of (and derivations of expectation and variance) uniform, binomial, geometric, negative binomial, Poisson and hypergeometric distributions
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Wednesday 10/5 |
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Finish important distributions
Begin review of discrete probability
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Thursday 10/6 |
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Review for Exam #1
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Friday 10/7 |
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Review for Exam #1
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Monday 10/10 |
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Exam #1 (in class)
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Wednesday 10/12 |
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Return Exam #1
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Friday 10/14 |
2.2, 6.3 |
Continuous probability
density functions
expectation and variance
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Monday 10/17 |
5.2 |
Important continuous Random Variables
Uniform and Normal
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Wednesday 10/19 |
5.2, 4.2 (Beta is in 4.2) |
More Important Random Variables
Exponential and Beta
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Friday 10/21 |
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Applications of continuous random variables
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Monday 10/24 |
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The DeMoivre-Laplace Limit Theorem
Opinion Polls
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Wednesday 10/26 |
7.2 |
Sums of Random Variables
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Friday 10/28 |
8.1 |
Chebychev’s Inequality
Law of Large Numbers
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Monday 10/31 |
9.1 |
The Central Limit Theorem
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Wednesday 11/2 |
11.1 |
Introduction to Markov Chains
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Friday 11/4 |
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Some Linear algebra
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Monday 11/7 |
11.4 |
Convergence of Markov Chains
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Wednesday 11/9 |
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Applications and Examples
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Friday 11/11 |
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Review for Final
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Monday 11/14 |
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Wrap Up
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11/18 |
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Review |