MATH 4426 Probability
Spring 2015

Dan Chambers   365 Carney

chambers@bc.edu    617-552-3769 (email is more reliable)

My Office Hours: Mondays 3-4, Wednesdays 12-1, Fridays 1-2, or by appointment.
Our TA, Tom Cremaschi (Carney 358) has hours Mondays 3-4, Wednesdays 12-1, Fridays 1-2.

Probability theory has a rich history, interesting mathematics, and many applications. In this class we will explore all of these. Topics include sample spaces; events;  conditional probability; independence; combinatorial probability; random variables; probability density functions; cumulative distribution functions; joint, marginal, and conditional pdf's; expected values; variances; higher moments; moment generating functions; order statistics; discrete distributions (including binomial, hypergeometric, Poisson, geometric, negative binomial);  continuous distributions (including normal, exponential, gamma); and the central limit theorem.

Here is a link to the syllabus.

This is a work in progress; check back for updates.

 Date topic/section HW assigned HW due/solutions January 12 2.2 sample spaces, algebra of sets calculus review problems solutions 14 2.2/2.3 distributive laws, DeMorgan's laws, definitions of probability, equal-likelihood experiments HW1 16 2.3 Kolmogorov's axioms, properties of a probability function 19 MLK Day 21 2.4 conditional probability 23 2.4 ct'd HW2 HW1 26 2.5 independence 28 snow day- BC canceled 30 2.5, 2.6 more independence, combinatorics February 2 snow day- BC canceled 4 2.6 more combinatorics HW3 HW2 6 2.6 concluded, 2.7 combinatorial probability 9/11 snow day; 3.2 binomial probabilities HW3 12 3.2 hypergeometric probabilities 13 3.3 discrete rv's, pdf/cdf 16 3.4 continuous rv's, pdf 18 3.4 continued HW#4 20 3.4, 3.5 begun, expected values 23 midterm 1  solutions 25 3.5 more expected values examples HW#4 27 3.5, 3.6 E(g(X)), variance March 2 spring break 4 spring break 6 spring break 9 3.6 variance HW#5 11 3.6, 3.7 higher moments, joint densities begun 13 3.7 joint densities- computing probabilities 16 3.7 independent rv's HW#5 18 3.7 more independence 20 3.8 combining rv's HW#6 23 3.9 further properties of the mean and variance 25 3.9 ct'd 27 3.10 order statistics (X_max, X_min) HW#6 30 class canceled April 1 class canceled 3 Easter break 6 Easter break 8 3.12 moment generating functions HW#7 10 3.12 mgf's 13 more mgf's 15 covariance HW#7 17 midterm 2 solutions 20 Patriots' Day 22 more covariance, Poisson distribution 24 more Poisson, normal distribution 27 CLT, normal approximation to binomial 29 geometric/negative binomial distributions chapter 4 problems     solns May 8 final exam 12:30 pm