Probability
STAT/MA 519, Fall 2012

Lecture: MWF, 9:30 AM -- 10:20 AM, in UNIV 117
(STAT 51900-003; Banner CRN 60149)
(MA 51900-004; Banner CRN 60148)

Professor: Mark Daniel Ward
Email: mdw@purdue.edu
Office: MATH 540
Phone: 765-496-9563

Office hours: Dr. Ward is always happy to meet with students.
Dr. Ward is available for walk-in or scheduled appointments anytime, throughout the week.
He is also always guaranteed to be available MWF, 8:30 AM -- 9:20 AM, in MATH 540.

Grader: Tian (Thomas) Qiu
Email: qiu30@purdue.edu

Course policy: click here

Midterm exam dates: Friday, October 5; Monday, November 19

Final exam date/time/location: Monday, December 10, from 1 PM to 3 PM in ME 2061

Plan to be present at all exams. Plan to be present for class every day.

Homework: Homework solutions will be collected in class on the due date. Homework solutions will be distributed in class.
Outline of Topics
Week 1: Mon, Aug 20
Introduction to the course,
discussion of policy, dates of exams,
other administrative issues,
sample spaces, events,
probability axioms
Wed, Aug 22
inclusion-exclusion,
equally-likely outcomes (intro only),
continuous set functions,
basics of a random variable
Problem Set 1 assigned,
due on Friday, Sep 7, at 9:30 AM
Fri, Aug 24
probability mass function,
expected value of a
random variable,
independence of two events,
independent vs disjoint
Week 2: Mon, Aug 27
independence of finitely many
or infinitely many events,
dependence of subsets,
dependence of complements,
sequences of trials,
probability of the first good trial
before the first bad trial
Wed, Aug 29
conditional probabilities,
independent random variables
Fri, Aug 31
calculating mass of one random
variable from the joint mass,
conditional mass,
indicator random variables
Week 3: Mon, Sep 3 (no lecture)
Labor Day
Wed, Sep 5
Bayes's Theorem with two events,
finitely many events,
or a countably infinite collection of events
Fri, Sep 7
brief review of independence,
conditional probabilities and masses,
introduction to variances and covariances,
Problem Set 1 due today at 9:30 AM,
Problem Set 2 assigned,
due on Wednesday, Sep 19, at 9:30 AM
Week 4: Mon, Sep 10
variance and covariance of
sums of random variables
Wed, Sep 12
covariances of sums of
two types of random variables,
conditional expectation,
expected value of a sum of
a random number of random variables
Fri, Sep 14
moment generating functions
Week 5: Mon, Sep 17
probability generating functions
extracting means and variances from GF's
introduction to geometric random variables
Wed, Sep 19
geometric and negative binomial random variables,
Problem Set 2 due today at 9:30 AM,
Problem Set 3 assigned,
due on Wednesday, Oct 3, at 9:30 AM
Fri, Sep 21
Poisson random variables
Week 6: Mon, Sep 24
connections between Poissons and
splitting into types,
more about hypergeometric random variables
Wed, Sep 26
Counting: Examples
Fri, Sep 28
Rules for Counting
Week 7: Mon, Oct 1
Questions about Problem Set 3,
Expected value and variance of the sum
of a random number of random variables
Wed, Oct 3
Review for Midterm Exam 1
Problem Set 3 due today at 9:30 AM
Fri, Oct 5
Midterm Exam 1
location to be announced
9:30 AM to 10:20 AM (usual time)
Week 8: Mon, Oct 8 (no lecture)
October Break
Wed, Oct 10
Review of Midterm Exam 1;
Introduction to continuous
random variables
Fri, Oct 12
Problem Set 4 assigned,
due on Wednesday, Oct 3, at 9:30 AM
Further introduction to
continuous random variables
Week 9: Mon, Oct 15
Examples about conditional densities
and how to move between joint densities
versus single-variable densities;
examples from qualifying exam questions
Wed, Oct 17
More examples of uniform distributions
in qualifying exams
Fri, Oct 19
Joint distributions of two random variables
that are each a function of two random variables
Week 10: Mon, Oct 22
Introduction to exponential random variables
Wed, Oct 24
Problem Set 4 due today at 9:30 AM
Problem Set 5 assigned,
due on Monday, Nov 5, at 9:30 AM
Introduction to Poisson Processes
Fri, Oct 26
Gamma random variables
Order statistics
Week 11: Mon, Oct 29
Normal Random Variables
Wed, Oct 31
Sum of independent Normal Random Variables
is a Normal Random Variable;
discussion of Problem Set 5
Fri, Nov 2
Central Limit Theorem,
Weak and Strong Laws of Large Numbers
Week 12: Mon, Nov 5
Normal random variables
Ward family dinner
Problem Set 5 due today at 9:30 AM
Problem Set 6 assigned,
due on Friday, Nov 16, at 9:30 AM
Wed, Nov 7
Conditioning
Fri, Nov 9
Conditioning,
and proof of the law of total variance
Week 13: Mon, Nov 12
proof of Strong Law of Large Numbers
Wed, Nov 14
questions from Problem Set 6,
CLT for non-iid random variables,
alternatives ways to calculate expected values
Fri, Nov 16
review for Midterm Exam 2
Problem Set 6 due today at 9:30 AM
Week 14: Mon, Nov 19
Midterm Exam 2
location to be announced
9:30 AM to 10:20 AM (usual time)
Wed, Nov 21 (no lecture)
Thanksgiving Vacation
Fri, Nov 23 (no lecture)
Thanksgiving Vacation
Week 15: Mon, Nov 26
review of Midterm Exam 2
functions of Uniform random variables
to construct other kinds of random variables
Problem Set 7 assigned,
due on Friday, Dec 7, at 9:30 AM
Wed, Nov 28
other distributions: beta, chi-squared,
Cauchy, bivariate normal
Fri, Nov 30
convergence in distribution
Week 16: Mon, Dec 3
more about convergence in distribution,
exchangeable random variables
Wed, Dec 5
review for Final Exam
Fri, Dec 7
review for Final Exam
Problem Set 7 due today at 9:30 AM
Final exam date/time/location: Monday, December 10, from 1 PM to 3 PM in ME 2061