Math 311 – Probability and Statistics,
MTR 12-1, Korman 249
information Grinstead & Snell History Tutoring
Week 1. Introduction
to the course. Division of stakes.
Finite probability framework. Venn diagrams. Monotonicity. Example.
De Méré’s bets. Uniform
distribution. Properties of probability. Tree diagrams. Algebra with
1.2. Problems. d’Alembert’s misstep.
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.
3. Cumulative distribution.
Examples. Quiz 2 (Chapter 2).
birthday problem. Permutations and combinations. Poker hands.
4. Bernoulli trials. Binomial
distribution. Binomial odds ratios. Inclusion-exclusion. Example. Quiz 3
Conditional probability (discrete
setting). Reverse tree
diagrams. Independence of events.
5. Questions session (Monday, 3-4:20PM, Curtis 457). Midterm 1 (1-3, 4.1). Bayes’
Monty Hall problem. Joint, marginal, and conditional probability mass
functions. Independence of random variables.
conditional probability. Mass vs density. Joint,
marginal, and conditional probability density functions. Example.
Joint cumulative distribution. Independence of continuous variables.
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.
8. Expected value and variance
(discrete and continuous settings). Quiz 5 (Chapter 5).
Reading: 6.1-6.3. Problems.
9. Sums of random variables. Convolution. Sum of binomials.
as a convolution. Reading: 7.1.
Office hours: Mon, Tue 12:05-2, Korman 249. Midterm 2 (4.2, 5, 6, 7.1).
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,
Dec 5. Final exam
(all lectures): Disque 108, 3:30-5:30 PM.