Week 1: | Mon, Aug 20 Introduction to the course, discussion of policy, dates of exams, other administrative issues, sample spaces, events, probability axioms |
Wed, Aug 22 inclusion-exclusion, equally-likely outcomes (intro only), continuous set functions, basics of a random variable Problem Set 1 assigned, due on Friday, Sep 7, at 9:30 AM |
Fri, Aug 24 probability mass function, expected value of a random variable, independence of two events, independent vs disjoint |
Week 2: | Mon, Aug 27 independence of finitely many or infinitely many events, dependence of subsets, dependence of complements, sequences of trials, probability of the first good trial before the first bad trial |
Wed, Aug 29 conditional probabilities, independent random variables |
Fri, Aug 31 calculating mass of one random variable from the joint mass, conditional mass, indicator random variables |
Week 3: | Mon, Sep 3 (no lecture) Labor Day |
Wed, Sep 5 Bayes's Theorem with two events, finitely many events, or a countably infinite collection of events |
Fri, Sep 7 brief review of independence, conditional probabilities and masses, introduction to variances and covariances, Problem Set 1 due today at 9:30 AM, Problem Set 2 assigned, due on Wednesday, Sep 19, at 9:30 AM |
Week 4: | Mon, Sep 10 variance and covariance of sums of random variables |
Wed, Sep 12 covariances of sums of two types of random variables, conditional expectation, expected value of a sum of a random number of random variables |
Fri, Sep 14 moment generating functions |
Week 5: | Mon, Sep 17 probability generating functions extracting means and variances from GF's introduction to geometric random variables |
Wed, Sep 19 geometric and negative binomial random variables, Problem Set 2 due today at 9:30 AM, Problem Set 3 assigned, due on Wednesday, Oct 3, at 9:30 AM |
Fri, Sep 21 Poisson random variables |
Week 6: | Mon, Sep 24 connections between Poissons and splitting into types, more about hypergeometric random variables |
Wed, Sep 26 Counting: Examples |
Fri, Sep 28 Rules for Counting |
Week 7: | Mon, Oct 1 Questions about Problem Set 3, Expected value and variance of the sum of a random number of random variables |
Wed, Oct 3 Review for Midterm Exam 1 Problem Set 3 due today at 9:30 AM |
Fri, Oct 5 Midterm Exam 1 location to be announced 9:30 AM to 10:20 AM (usual time) |
Week 8: | Mon, Oct 8 (no lecture) October Break |
Wed, Oct 10 Review of Midterm Exam 1; Introduction to continuous random variables |
Fri, Oct 12 Problem Set 4 assigned, due on Wednesday, Oct 3, at 9:30 AM Further introduction to continuous random variables |
Week 9: | Mon, Oct 15 Examples about conditional densities and how to move between joint densities versus single-variable densities; examples from qualifying exam questions |
Wed, Oct 17 More examples of uniform distributions in qualifying exams |
Fri, Oct 19 Joint distributions of two random variables that are each a function of two random variables |
Week 10: | Mon, Oct 22 Introduction to exponential random variables |
Wed, Oct 24 Problem Set 4 due today at 9:30 AM Problem Set 5 assigned, due on Monday, Nov 5, at 9:30 AM Introduction to Poisson Processes |
Fri, Oct 26 Gamma random variables Order statistics |
Week 11: | Mon, Oct 29 Normal Random Variables |
Wed, Oct 31 Sum of independent Normal Random Variables is a Normal Random Variable; discussion of Problem Set 5 |
Fri, Nov 2 Central Limit Theorem, Weak and Strong Laws of Large Numbers |
Week 12: | Mon, Nov 5 Normal random variables Ward family dinner Problem Set 5 due today at 9:30 AM Problem Set 6 assigned, due on Friday, Nov 16, at 9:30 AM |
Wed, Nov 7 Conditioning |
Fri, Nov 9 Conditioning, and proof of the law of total variance |
Week 13: | Mon, Nov 12 proof of Strong Law of Large Numbers |
Wed, Nov 14 questions from Problem Set 6, CLT for non-iid random variables, alternatives ways to calculate expected values |
Fri, Nov 16 review for Midterm Exam 2 Problem Set 6 due today at 9:30 AM |
Week 14: | Mon, Nov 19 Midterm Exam 2 location to be announced 9:30 AM to 10:20 AM (usual time) |
Wed, Nov 21 (no lecture) Thanksgiving Vacation |
Fri, Nov 23 (no lecture) Thanksgiving Vacation |
Week 15: | Mon, Nov 26 review of Midterm Exam 2 functions of Uniform random variables to construct other kinds of random variables Problem Set 7 assigned, due on Friday, Dec 7, at 9:30 AM |
Wed, Nov 28 other distributions: beta, chi-squared, Cauchy, bivariate normal |
Fri, Nov 30 convergence in distribution |
Week 16: | Mon, Dec 3 more about convergence in distribution, exchangeable random variables |
Wed, Dec 5 review for Final Exam |
Fri, Dec 7 review for Final Exam Problem Set 7 due today at 9:30 AM |
Final exam date/time/location: Monday, December 10, from 1 PM to 3 PM in ME 2061 |