| 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 Inclusion-Exclusion
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 DeMoivre-Laplace 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 |