## Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in the Homework assignments page will always be accurate.

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