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