Stat 530-531 / Math 546-547 -- graduate level introduction to probability theory.
GENERAL DESCRIPTION:
Graduate level means ``with proofs, based on theory of
Lebesgue mesaure and integration''. It does not mean
``without intuition'' nor ``purely formal''.
Compare to Stat 510. There they use Ross. He does not
even prove our first result (Strong Law of Large Numbers)
except in finite variance case. Furthermore, even if
you don't care about proofs, he does not even state many
(most!) critical results on which classical statistical
tests are based, e.g., LIL, large deviations, any theorem
or criterion for Poisson approximation to be valid, etc.
HOW TO DECIDE IF YOU HAVE THE PRE-REQUISITES FOR THIS COURSE:
Students sometimes need some help deciding whether this is
the right course for them. If you are in doubt, have a look
at the textual materials and the first homework (already posted)
and see whether you can envision being comfortable with that
material within a few weeks. In general, facility with writing
mathematical proofs at the level of math 360-361 is going to be
much more important than any specific mathematical or statistical
knowledge. Mathematical analysis at the level of Penn's Math 508-509
is recommended and if you've had measure theory you'll be glad of it,
but many students have not had this and in principle an
undergraduate level analysis course such as Penn's Math 360-361
should be sufficient, PROVIDED YOU LEARNED IT WELL. Most students
have had undergraduate probability but those who have not usually
do fine. Students who have not learned analysis well at the
basic level (Penn 360-361) will struggle mightily.