Math 361 X1 Course Web Page

Course Information Sheet

Final Exam (Scores are in!)

Score Reports: Click here to access your score on the final and your course grade. Your course grade is the grade shown as "average" at the end of the score display (with plusses and minuses).
Final exam results and grading information: The average (raw) score on the final was 60 points (out of 100). The highest scores were 95, 93, 92; the lowest scores 28, 32, 33, 35. The final was curved using 78/60/42/24 as cutoffs for A/B/C/D. If are still in town and want to see your final exam, stop by my office, 241 Illini Hall, today (Friday, May 16) after 3 pm, or Monday (May 19) afternoon. Otherwise enjoy your summer!
Final Exam Information Sheet

Reading Guide to the Pitman Text

A page-by-page guide to the Pitman text, which tells you which sections/subsections to concentrate on, and which parts you can skip. It also lists problems from the text recommended for additional practice.

Supplementary materials

Double Integrals. A set of tips and practice problems for double integrals, with special emphasis on integrals that typically occur in probability computations. Solutions are available under this link.
Joint Continuous Distributions. A summary of definitions, properties, and formulas associated with continuous joint distributions.
Continuous Random Variables. A class handout (4/16) with essential formulas for continuous random variables, their densities and distribution functions (c.d.f.'s).
Normal approximation to sums of independent random variables (central limit theorem)> This very interesting applet lets you reproduce graphs of successive sums of i.i.d. random variables like those on p. 200 - 201 of the book. You can specify the initial distribution by assigning probabilities for (up to) 10 values P(0), P(1), P(2), ..., P(9). The program then computes and plots, for given n, the distribution of a sum of n independent r.v.'s having this distribution. It is remarkable how quickly the distribution approaches the normal shape, if you start with n = 1 (the original distribution), then take n=2, n=3, etc.
Normal approximation, II: A handout from class (4/2) on the normal approximation to sums of independent random variables (Section 3.3 in Pitman).
Normal Approximation, I. A handout distributed on 2/14, summarizing the formulas for the normal approximation to the binomial distribution.
Normal vs. Poisson Approximation. Another class handout from 2/14, showing how the normal and the Poisson approximations compare in the case n=100, for various choices of the values p and k.
Normal approximation. A java applet that, for given values of n and p and a given range for k, plots the binomial distribution along with the approximating normal curve. The match is remarkably good, even if n is relatively small.
Plot of the Binomial Distribution This java applet allows you to plot the binomial distribution for a given value of p and three values of n.
Coin tossing simulation. This applet simulates a sequence of coin tosses and plots the accumulated "scores" (1 for a head, -1 for a tail).
Variations on the birthday theme A handout with two problems related to the birthday problem.
Java simulation of the birthday problem. Very nice.
The Car/Goat (Monty Hall) Problem. A separate webpage with links to handouts distributed in class, to websites containing some nice java simulations, and to a New York Times article on the history and origins of the problem.
Sampler of Problems. A handout given out the first day of class.

Historical links, quotes, and miscellany

Links to pictures and biographies of some of the great names in probability, and some choice quotes.

Announcements

4/25/03: Exam 3: The third and final hour exam will be in class on Friday, May 2, in the regular class room. The exam will cover the material since the last exam through the end of Chapter 4, but not Chapter 5. For more details see the Exam Review Guide.
4/25/03: Solutions to the Double Integrals Handout. A link to a pdf file with solutions to the problems on the Double Integrals handout that was passed out on Monday.
3/28/03: Exam 2: The next hour exam will be in class on Friday, April 4, in the regular class room. The exam will cover Chapter 3, with the exception of 3.3, and combinatorial probabilities. I have posted a detailed Exam Review Guide.
3/12/03: Math/Stat 308 Exam. Today I had an exam in the other probability class I am teaching, Math/Stat 308, Introduction to Actuarial Statistics. This is a class that covers roughly the same material as Math 361, though at a somewhat lower level and geared towards the needs of students in Actuarial Science. Except for one problem (Problem 8), which involves so-called moment-generating functions, all problems deal with material we have covered in 361, so you should have no difficulty with this exam. Give it a try! Solutions are also available.
3/5/03: Room change on EOH day (March 14): Because of the Engineering Open House, the regular classroom will not available on Friday, March 14. The class will be held instead in Room 140 Burrill. I am not yet decided on what to do that day. In any case I don't plan on covering regular class material, or anything that might show up on exams, for that matter. Perhaps a topic that is interesting but doesn't fit into the regular syllabus. Or maybe an "open house" style q&a session. Or not meet at all ...
3/3/03: Extracredit Projects: A new webpage with a description of possible extracredit projects, and the modalities for doing such a project. In particular, the deadline for taking an EC project is April 7, and the deadline for turning in the project is May 5.
3/1/03: Homework 5 posted: For those who want to get an early start on next week's homework assignment, the homework assignment is now up, and so are hints.
2/23/03: Reading Guide to the Pitman Text. I have compiled the individual reading guides accompanying the class summaries into a single web page that covers (at present) Chapters 1 and 2.
2/21/03: Homework next week. Because of the exam, there will be no homework assignment next week. The next assignment will be due the following week.
2/19/03: Exam 1. The first hour exam will be held, as scheduled, Friday, Feb. 28, 12 - 1, in the regular classroom. It will cover Chapters 1 and 2. I have posted a detailed Exam Review Guide.
2/16/03: Course Web Page expanded. I have re-organized the course webpage (this page), and added a number of links and related materials. In particular, in the section "Supplementary materials" I have added links to several java simulations of the binomial distribution and the normal approximation, and pdf versions of Friday's class handouts. I have also added a new section, "Historical links", with links to biographies of famous probabilists (Kolmogorov, Poisson, Bayes, ...), and some quotes.
2/13/03: Undergraduate Math Talk, Wednesday, 2/19, 4:30 pm, 245 Altgeld Hall. Professor Ed Burger of Williams College will give a lecture suitable for undergraduate math majors, on "How to Always Win at Limbo". More information about this talk can be found here.
2/12/03: Car/Goat web page: I have added a link to a complete solution to the car/goat problem (which I worked out in class on 2/5).
2/2/03: Homework 2 posted: For those who want to get a headstart, I have now posted the second HW assignment (due Friday, 2/7). I will pass out hard copies in Monday's class. Hints will be posted in a day or two. All except the final two problems depend only on the material covered through the end of last week. Problem 1 is of the same type as the problems in the first HW assignment. Solutions to that assignement have been posted and will be handed out in Monday's class. Problems 2 - 4 are theoretical exercises similar to those I did in Friday's class; I will do one or two more examples on Monday. The final two problems are word problems involving conditional probabilities and Bayes' rule; I will cover problems of this type in Monday's class.
2/2/03: Open House: As mentioned in class, I have set aside a time and reserved a room for a weekly "Open House" for students in the two classes I am teaching, Math/Stat 308, and Math 361/Stat 351. (Math 308 is a probability theory class for actuarial students.) The open house will be Wednesdays, 6 pm - 7 pm, in Room 141 Altgeld Hall.
2/2/03: Email contact: When sending me email (at ajh@uiuc.edu), put the class number (Math 361) somewhere in the subject line. The purpose of this is threefold: First, it will tell me that you are a student in one of my classes, and you are more likely to receive a prompt reply than with a non-descriptive subject line. I receive a fair amount of email, but I try to take care of student email right away. Second, it tells me which class you are in. (This is important since I am teaching two classes.) Finally, it causes the message to be filed into an appropriate folder.

Homeworks Assignments

Class Summaries

Brief summaries of what I did in class, usually accompanied by a "Reading Guide" to the corresponding section in the Pitman text.

Reading Guide to the Pitman Text

A detailed, page-by-page reading guide to the sections in the Pitman text covered in class, along with a list of suggested practice problems from the text. Some topics in the text are more important than others, and there are some parts that you can skip entirely. The reading guide tells you which sections/topics/examples/problems to focus on when reviewing the material from the book. (This is a compilation of the individual reading guides posted under "Class Summaries".)

Last modified Fri 11 Feb 2005 12:45:19 PM CST ajh@uiuc.edu

Math 361 X1 Course Web Page

Course Information Sheet

Final Exam (Scores are in!)

Exam 3

Exam 2

Exam 1

Reading Guide to the Pitman Text

Supplementary materials

Historical links, quotes, and miscellany

Announcements

Homeworks Assignments

Class Summaries

Reading Guide to the Pitman Text