MATH 671, FALL 2003
Probability Theory I
MWF 9:05 -- 9:55 , 207 Malott
Greg Lawler, 567 Malott
TA, Hasan Sayit
Office Hours: Greg Lawler, M 2:45 - 3:45, W 1:30 - 2:30, Th 2:30 - 3:30,
567 Malott
Hasan Sayit T 4:00 -- 6:00, 218 Malott
This is an introduction to measure theoretic probability
for students who have seen measure theory, We will
disuss probability spaces, laws of large numbers,
central limit theorem, (discrete time) martingales,
and an introduction to Brownian motion.
Texts
Durrett, Probability: Theory and examples.
We will focus on Chapters 1,2,4,7
Final Problem Set
I will hand out the final problem set on Wednesday,
December 3. However, since some people requested it
sooner, I will post a DRAFT of the problems. Even if
you start working on the problems now, it is important
that you pick up the version on Wednesday because there
may be some changes/corrections.
This is
the version handed out in class.
Here are some corrections:
Please ignore the previous correction to Problem 5 (or
you may do the corrected problem). At this point I will
accept either one!
On Problem 1, the last X on the first line should
be X_1.
Homework
HW assignments will be given in the lectures.
Solutions will be handed in on Wednesday of the following week
(unless mentioned otherwise).
The assignments will be listed on this page.
PS 1 (due 9/10): p. 12, 2.3; p. 22, 3.16; p. 34, 4.13 and
the following extra problem: Suppose F_0 is a field of subsets
generating sigma-field F on a probability space (Omega,F,P).
Show that for every A \in F and every \epsilon > 0,
there is an A_0 \in F_0 such that P(A\A_0) + P(A_0\A) <
\epsilon.
PS 2 (due 9/17): p. 46, 5.3, 5.5, 5.6; p. 55, 6.12, 6.13, 6.18
PS 3 (due 9/24) p. 61, 7.3; p. 84, 2.1; pp. 90--91, 2.6, 2.8, 2.9,
2.13
PS 4 (due 10/1) p.95, 3.1; p.98, 3.5; p. 99, 3.8; p. 101, 3.12, 3.14;
p. 104, 3.20
PS 5 (due 10/15) p. 115, 4.2; p. 121, 4.9, 4.11;
p. 139: 6.1, 6.2; p. 148, 6.7, 6.12
PS 6 (due 10/22) P. 229, 1.10, p. 237, 2.4; ISP: 5.2, 5.3
PS 7 (due 10/29) p. 238, 2.9, 2.11; p. 265, 5.8;
ISP: 5.5/5.10, 5.14
PS 8 (due 11/5) p. 275, 7.2, 7.5; p. 240, 3.2;
p. 249, 3.13, ISP, 5.9
PS 9 (due 11/12) p. 74, 9.3; p.76, 9.5; p. 78, 9.8
There will be a long final problem set in lieu of a final
examination.
EXCEPT FOR THE FINAL PROBLEM SET,
students may discuss homeworks with each other (and others)
but should write solutions themselves. The final problem
set should be done without consulting others (but any books
or other written material may be consulted).
Last modified: 05 December 03