MT426 Probability
Spring 2010

Prof.  Dan Chambers  
Office:  365 Carney
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.

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
2.7 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
exam 1
3.4 continuous rv's
Mar. 1-5
spring break
spring break
spring break
Mar. 8-12
3.4 HW#5 solns
3.5 expected values
Mar. 15-19
3.6 variances
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
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