Math 3225, Honors Prob. and Stats, Fall 2010
For a copy of the course syllabus, click
here
Click here for some notes.
Click here for some additional lecture
notes (most of which I will not cover).
I have decided to add two office hours: Let's say Thursdays from 1:051:55,
and Wednesdays from 2:05  2:55 (after class).
For a copy of the notes on the Lovasz Local Lemma, click
here .
For a note on the ``Birthday problem'' about 23 people sharing a
birthday, see this note .
Homework 1 (to be turned in Friday, Sept. 24)

Click here for the first HW.


For a copy of lecture note 3, click here .
For a link to the BanachTarski Paradox from class, click
here .
For a note on the ``two slips of paper'' puzzle from class today,
click here .
Homework 2 (to be turned in with the exam Oct. 13).

Click here for a copy of the
second homework.

Click here for a
note on Bayesian Spam filtering from class today.

Click here for some notes
on random variables and probability density functions.

Click here for some notes
on Bernoulli and Binomial random variables.


Click here for a
note on Poisson Processes.

Click here for a note
on the Poisson distribution and Poisson random variables (continues
on from the previous note).

Homework 3 (due Monday, Nov. 8).

Click here for lecture notes
on the Erdos Multiplication Table Theorem, and Chebyshev's inequality
and Markov's inequality.

Click here for a note on
some facts about the expectation operator.

Click here for the new HW.

Click here for notes on the
chisquared distribution.

Click here for some
notes on applications of the central limit theorem.

Click here for the
``two portfolios'' example from class today.
Homework 4 (Wednesday, November 24 (turn in with midterm) ).

Here are a few popular math articles related to statistics:
Click here for a generalaudience essay about ``Zipf's Law''; click here for an article on how the IRS uses Benford's Law to catch tax cheats. Click here for a generalaudience essay about prime numbers and energy levels; and click here for a related article which appeared in the American Scientist. Click here for an journal publication about ``binocular rivalry'', consciousness and quantum formalism (Note: The article is not asserting that the mind arises from `quantum processes'  it is only asserting that the same math used to describe quantum phenomena can be used to model the binocular rivalry phenomenon.). Click here for an article on ``Random Matrix Theory: a law that explains everything''. Click here for an article on ``The BihamMiddletonLevine Traffic Model'', and the strange statistical distributions that arise in traffic jams. Finally, click here for an article on ``universality''.

Click here for a
note on confidence intervals for the mean and variance of a standard
normal (and pay attention to the bit of history!).

Click here for a copy of the fourth HW.

Click here for a note on
maximum likelihood estimates and least squares estimates.

Click here for a note on the
correlation coefficient.

Click here for some advice
for students planning on attending graduate school in mathematics.



For a note on hypothesis testing, click here .


*** Note: I left off the sample standard deviation from probelm
5 in the hw (I miscopied the problem from the book I took it from). I
have now added this to the hw4 above. ***

Click here for a note on the Pagerank algorithm.

Click here for a note on
Hidden Markov Models.

Click here for the first
set on notes on Markov Chains.

Click here for an example
of an old Final Exam.

Click here for
some practice problems on Markov chains.

Click here for a note on
Markov Chains notes part 2.

As promised, here is the reference to the probability book for
the Brownian Motion material: Introduction to Probability Models, Eighth
Edition, by Sheldon Moss.

Click here for a study
sheet for the final exam.