MATH 4426 Probability
Spring 2018

Dan Chambers   543 Maloney Hall

chambers@bc.edu    2-3769 (email is more reliable)

My Office Hours: Mondays 3-4, Wednesdays 2-3, Fridays 11-12, or by appointment.

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 17 2.2 sample spaces, algebra of sets calculus review solutions 19 2.2/2.3 distributive laws, DeMorgan's laws, definitions of probability, equal-likelihood experiments HW1 22 2.3 Kolmogorov's axioms, properties of a probability function 24 2.4 conditional probability 26 2.4 ct'd HW2 HW1 29 2.5 independence 31 2.5 more independence February 2 2.6 combinatorics- permutations HW2 5 2.6 combinatorics- combinations HW3 7 2.6 concluded 9 2.7 combinatorial probability 12 2.7 the hat problem HW3 14 3.2 binomial distribution HW4 16 3.2 hypergeometric distribution 19 3.3 discrete random variables 21 3.4 continuous random variables HW4 23 midterm 1 solutions 1A  solutions 1B 26 3.4 ctd 28 3.4/3.5 expected value HW5 March 2 3.5 5 spring break 7 spring break 9 spring break 12 3.6 variance 14 3.6 ct'd, E(g(X)), higher moments HW5 16 3.7 joint densities 19 3.7 ct'd 21 class cancelled HW6 23 3.8 combining rv's 26 3.9 further properties of the mean and variance 28 3.9 ct'd HW7 30 Easter break April 2 Easter break 4 3.10 order statistics (X_max, X_min) HW6 6 3.12 moment generating functions 9 3.12 ct'd HW7 11 midterm 2 solutions 2A  solutions 2b 13 3.12 ct'd HW8 16 Patriot's Day 18 4.2 Poisson 20 4.2 Poisson 23 4.3 Normal HW8 25 4.3 Normal 27 4.4 Geometric 30 4.5 Negative binomial chapter 4 practice problems practice problem solutions May 2 wrap up