MT426 Probability
Spring 2010

Prof.  Dan Chambers
Office:  365 Carney
chambers@bc.edu
617-552-3769 (email is more reliable)

Probability 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 (binomial, hypergeometric, Poisson, geometric, negative binomial);  continuous distributions (normal, exponential, gamma); and the central limit theorem.

Office Hours: Monday 11-12, Wednesday 1-2, Friday 3-4, or by appointment.

The text we'll use is An Introduction to Mathematical Statistics and Its Applications, 4th Edition, by Richard Larsen and Morris Marx. We'll cover the first four chapters. Here is a copy of the syllabus. Here are calculus for probability
review problems.

 Week Monday Wednesday Friday Jan. 18-22 2.2 sample spaces, algebra of sets 2.2/2.3 distributive laws, DeMorgan's laws, definitions of probability, equal-likelihood experiments HW#1  solns Jan. 25-29 2.3 Kolmogorov's axioms, properties of a probability function 2.4 conditional probability 2.4 ct'd Feb. 1-5 2.5 independence HW#2   solns 2.5, 2.6 more independence, combinatorics 2.6 more combinatorics Feb. 8-12 2.6 2.7 combinatorial probability HW#3 solns 2.7 more combinatorial probability Feb. 15-19 3.2 binomial distribution 3.2 hypergeometric distribution HW#4  solns 3.3 discrete rv's Feb. 22-26 3.3 exam 1 3.4 continuous rv's Mar. 1-5 spring break spring break spring break Mar. 8-12 3.4 3.4 HW#5 solns 3.5 expected values Mar. 15-19 3.5 3.6 variances 3.6 HW#6 solns Mar. 22-26 3.7 joint densities 3.7 ct'd 3.8 distribution of sum, quotient, product of two independent rv's Mar. 29-Apr. 2 3.9 more properties of E and V HW#7 solns 3.9 ct'd Easter break Apr. 5-9 Easter break 3.10 order statistics (X_max, X_min, arbitrary) 3.10 (joint density of X_max, X_min)  3.11 conditional densities (briefly) Apr. 12-16 3.12 mgf's exam 2 3.12 ct'd Apr. 19-23 Patriot's Day 3.12 4.3 normal distribution introduction HW#8 solns Apr. 26-30 4.3 normal 4.3 normal 4.3 CLT and examples May 3-7 normal approximation to binomial solns to normal dist. problems applications of probability to statistics: confidence intervals, hypothesis testing