Probability Theory (AMS 311) Course Material, Fall 2009
The course meets Tues/Thurs, 9:50 -- 11:10, in
Library W4550.
Joe's Office Hours:
Tues (1:00-2:30) and Wed (3:00-4:00),
and please drop by any time, or send email or call
Exam2 will be in class on Thursday, Nov 12.
Last names beginning with "A" through "G" take the exam in Library E-4310;
last names beginning with "H" through "Z" take the exam in Library W-4550 (the usual classroom).
10/26/09: I corrected an error in hw4-solutions: problem 1(b).
We have 2 TA's for the course:
Changsoon (Alex) Yong (a.yong1204@gmail.com), 10:00-11:00 (Mon), 5:30-6:30 (Wed); and
KwangHyun Park (pkhsite@gmail.com), 5:30-6:30 (Mon), 5:30-6:30 (Tues).
The TAs hold office hours in Harriman 010.
Main Course Information
Course Information (AMS 311), Fall 2009 This is the main
course information sheet with details about exams, homeworks, grading, etc.
Homeworks and Other Handouts
Homework 1, due Thursday 9/10/09;
( Solutions, posted after due date)
Homework 2, due Thursday 9/17/09;
( Solutions, posted after due date)
Homework 3, due Thursday 9/24/09,
( Solutions, posted after due date)
Practice Exam 1 (actually THREE practice exams here);
Solutions
Notes and examples on discrete distributions
Notes on continuous distributions
Homework 4, due Thursday 10/22/09,
( Solutions, posted after due date)
Homework 5, due Thursday 10/29/09,
( Solutions, posted after due date)
Notes on Expectation, Moment Generating Functions, Variance, and Covariance
Homework 6, due Thursday 11/5/09,
( Solutions, posted after due date)
Practice Exam 2 (actually THREE practice exams here);
Solutions
Examples of joint pdf problems, some/many solved in class.
Review list for Exam 2
Cover sheet of Exam 2, showing what formulas will be there, instructions,
etc.
Homework 7, due Tuesday 11/24/09,
( Solutions, posted after due date)
An On-Line Interactive Textbook with Examples
Virtual Laboratories in Probability and Statistics, by Kyle Siegrist.
Very nice and extensive interactive "text" on probability and statistics.
Lots of examples.
Links of Interest to the Course:
Compendium of Probability Distributions
Let's Make a Deal applet
Brief report on Monty Hall problem, by Afra Zomorodian
Probability by Surprise
Cut-the-Knot Probability Page
Chance Web Page, real-life uses of probability and statistics
(co-authored by my office-mate from Stanford, Bill Peterson)
Nick's Mathematical Puzzles, with several nice probability puzzles,
including some classics!
Conditional Probability Discussion
For Your Amusement:
I know two distinct secret numbers: call them X and Y, and assume
that X < Y, without loss of generality. You have no clue how I came
up with them. They could be anything (positive, negative, rational,
irrational, etc). They could come from any probability distribution
(discrete or continuous). You have no idea. I flip a fair coin. If
the coin shows Heads, I reveal to you the larger number, Y; if it
shows Tails, I reveal to you the smaller number, X. You do not get
to see the result of the coin flip. Your goal is to guess whether the
coin was Heads or Tails, based only on your seeing the one number that
I revealed to you. Obviously, if you just decide ``Heads'' is your
guess, without taking into account the revealed number at all, then
you are correct with probability 0.5. But your goal is to be able to
be correct with probability {\em strictly greater} than 0.5. Devise a
method to do this, and explain your solution.
The three way pistol duel puzzle:
You're a cowboy, and get involved in a three way pistol duel with two other
cowboys. You are a poor shot, with an accuracy of only 33%. The other two
cowboys shoot with accuracies of 50% and 100%, respectively. The rules of
the duel are one shot per cowboy per round. The shooting order is from worst
shooter to best shooter, so you get to shoot first, the 50% guy goes second,
and the 100% guy goes third, then repeat. If a cowboy is shot he's out for
good, and his turn is skipped. Where or who should you shoot first?
You have two ropes. Each takes exactly 60 minutes to burn. They are
made of different material so even though they take the same amount of
time to burn, they burn at separate rates. In addition, each rope burns
inconsistently. How do you measure out exactly 45 minutes?
(You are to assume that, while the speed of the rope burning
may vary with position x along the rope, the speed of burning
to the right at x is the same as the speed of burning to the left at x.)
Two engineering students had thoroughly impressed their Professor
in one of their core subjects, having achieved the highest marks
throughout the semester's continuous assessments. Being one to give
credit where due, the Prof made no secret of his two prize students,
continually praising their achievements.
The weekend before their final exam (which was to contribute
fifty percent of their final grade,) these two geniuses felt they
deserved a hard earned break and so went out of town to celebrate
their 'pending' success.
Having partied late all weekend (and then some,) the two students
overslept Monday morning, missing their final exam! Never lacking
in will power, they were determined not to fail, having come so far,
so well. Upon rolling into town, they appealed to the Prof, and
conveniently explained that they had a flat tire while out visiting
and that it was not their fault for missing the exam.
The Professor was very understanding and rescheduled their exam
to the next day, much to the student's delight! They arrived at his
office the next morning, where he sat them on each side of his desk
facing opposite walls, while he worked on grading the other exams.
They opened their examination books and were both pleased with the
first easy 10-point question that came directly from a homework
assignment. You could hear nothing but the quick writing of their
pencils in the room, until they both flipped the page, almost at
the same time, where the second question read thusly...
"90 points: Which tire?"