Lectures 
Sections in Text 
Brief Description 
Monday 9/12 

Course topic and objectives
Course details: office hours, grades, exams, HW
Teamwork exercise: the Josephus Problem

Wednesday 9/14 
1.2 
Basic concepts and language: experiment, outcome, sample space, probability
distribution, uniform distribution, independent trials, law of large numbers,
event

Friday 9/16 

Multiple event probabilities (union, complement,…)
Random Variable (numerical function on a sample space)
Distribution of a random variable
Odds

Monday 9/19 
3.2 
HW #1 Due
Subsets, binomial coefficient, Pascal’s triangle, binomial theorem
Binomial distribution

Wednesday 9/21 

Riffle shuffling

Friday 9/23 
3.1 
Permutations, factorial, Stirling’s Formula
Principle of InclusionExclusion
Hat Check Problem

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

Wednesday 9/28 

Independent Random Variables
Expectation and variance of a random variable, examples
Expectation linear always, variance additive if independent

Thursday 9/29 

Applications of linearity of expectation
ESP problem
Buffon’s Needle

Friday 9/30 

Bayes’ Formula, examples
Further examples of conditional probability

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

Wednesday 10/5 

Finish important distributions
Begin review of discrete probability

Thursday 10/6 

Review for Exam #1

Friday 10/7 

Review for Exam #1

Monday 10/10 

Exam #1 (in class)

Wednesday 10/12 

Return Exam #1

Friday 10/14 
2.2, 6.3 
Continuous probability
density functions
expectation and variance

Monday 10/17 
5.2 
Important continuous Random Variables
Uniform and Normal

Wednesday 10/19 
5.2, 4.2 (Beta is in 4.2) 
More Important Random Variables
Exponential and Beta

Friday 10/21 

Applications of continuous random variables

Monday 10/24 

The DeMoivreLaplace Limit Theorem
Opinion Polls

Wednesday 10/26 
7.2 
Sums of Random Variables

Friday 10/28 
8.1 
Chebychev’s Inequality
Law of Large Numbers

Monday 10/31 
9.1 
The Central Limit Theorem

Wednesday 11/2 
11.1 
Introduction to Markov Chains

Friday 11/4 

Some Linear algebra

Monday 11/7 
11.4 
Convergence of Markov Chains

Wednesday 11/9 

Applications and Examples

Friday 11/11 

Review for Final

Monday 11/14 

Wrap Up

11/18 

Review 