Math 311 – Probability and Statistics, Fall 2016

    

Instructor: Anatolii Grinshpan

Office hours:  MTR 12-1, Korman 249

Course information   Grinstead & Snell    History    Tutoring center


Week 1.  Introduction to the course.  Division of stakes. Finite probability framework. Venn diagramsMonotonicityExample.
               De Méré’s bets. Uniform distribution. Properties of probability. Tree diagrams. Algebra with events.

               Reading: 1.1, 1.2Problems. d’Alembert’s misstep.

 

Week 2.  Quiz 1 (Chapter 1). Question. Coin toss until first head. Continuous probability model. Uniform distribution. Monte Carlo procedure.

               Buffon’s needle. Bertrand’s paradox. The density function. Examples.

               Reading: 2.1, 2.2. Problems.

 

Week 3.  Cumulative distribution. Examples. Quiz 2 (Chapter 2).

               Combinatorics. The birthday problem. Permutations and combinations. Poker hands.

               Reading: 3.1, 3.2. Problems.

 

Week 4.  Bernoulli trials. Binomial distribution.  Binomial odds ratios.  Inclusion-exclusion. Example. Quiz 3 (Chapter 3).

               Conditional probability (discrete setting). Reverse tree diagrams. Independence of events.

               Reading: 4.1.

 

Week 5.  Questions session (Monday, 3-4:20PM, Curtis 457). Midterm 1 (1-3, 4.1).  Bayes’ formula.

               Monty Hall problem. Joint, marginal, and conditional probability mass functions. Independence of random variables. 

               Reading: 4.1. Problems.

 

Week 6.  Continuous conditional probability. Mass vs density. Joint, marginal, and conditional probability density functions. Example.

               Joint cumulative distribution. Independence of continuous variables.

               Reading: 4.2.

 

Week 7.  Quiz 4 (Chapter 4). Some common probability mass and density functions. Multinomial distribution. Poisson distribution.

               Cauchy density. Random coin. Poisson counts and exponential waiting times.

               Reading: 5.1, 5.2. Problems.

              

Week 8.  Expected value and variance (discrete and continuous settings). Quiz 5 (Chapter 5).

               Reading: 6.1-6.3Problems.

 

Week 9.  Sums of random variables. Convolution. Sum of binomials. Binomial as a convolution. Reading: 7.1.

               Office hours: Mon, Tue 12:05-2, Korman 249. Midterm 2 (4.2, 5, 6, 7.1).  

 

Week 10. Sums of continuous variables: exponential, uniform, normal. The Law of Large Numbers. Chebyshev’s inequality.

                Reading: 7.2, 8.1, 8.2. Quiz.

 

Week 11. Monte Carlo. The Central Limit Theorem. De Moivre-Laplace. Spike plots.  Local Limit Theorem.

                Reading: 9.1-9.3. Problems. Chicago train.

                Office hours: Th 12:05-2, Friday 11-1,  Korman 249.

 

Dec  5.    Final exam  (all lectures): Disque 108, 3:30-5:30 PM.