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