STA 247 - Probability with Computer Applications (Sept-Dec 2003)

Assignments 2 and 3 have now been marked, and can be picked up January 8 from 3:00-3:30, or in my office hours starting the next week, which are Tuesdays 2:30-3:30, Thursdays 2:30-3:30, and Fridays 10:10-11:00.

There were initially some problems marking Assignment 2, so if you've already picked up this assignment, you may wish to give it back to me to see if the mark should be changed.

A listing of term marks is available here, which now includes Assignment 3. Please inform me of any errors.

This course is an introduction to probability with an emphasis on topics relevant to computer science. Small programming assignments will be used to illustrate applications in computer science and to reinforce concepts of probability.

The follow-on course is STA 248, which will cover statistical inference. Together, STA 247 plus STA 248 will be accepted as equivalent to STA 250 plus STA 255 as prerequisites to most higher-level statistics courses (eg, STA 302), although this was mistakenly omitted from the calendar.

Instructor: Radford Neal, Office: SS6016A, Phone: (416) 978-4970, Email:


Mondays, Wednesdays, and Fridays, 3:10pm to 4:00pm, from September 8 to December 5, except for Thanksgiving (October 13). Held in Alumni Hall (AH), Room 100 (east of Queen's Park).


James J. Higgins and Sallie Keller-McNulty, Concepts in Probability and Stochastic Modeling, Wadsworth, 1995.

Here is a list of typos for the book.


There will be some small computing exercises, in the R language, which you can do on the CQUEST computer system, which can be accessed from various locations on campus, or from home. Click here to request an account on CQUEST.

STA 247 has a CQUEST page, which tells you how to use R.


Final exam: 55% (Scheduled by the Faculty)
Mid-term test: 15% (Wednesday, October 15, 3-4pm)
Assignments: 30% (three assignments, worth 10% each, due Nov. 3, Nov. 24, Dec. 5)

Reading list:

Chapter 1: all
Chapter 2: all
Chapter 3: 3.1, 3.2, 3.5
Chapter 4: 4.1, 4.2, 4.3 4.4, 4.5
Chapter 5: 5.1, 5.2
Chapter 6: 6.1, 6.2
Chapter 8: 8.1, 8.2
I will also cover some other topics regarding computer applications, and introduce you to the R language. Informaton on these topics will be provided by hardcopy handouts or on the web.

Non-credit exercises to do:

1.2-3, 1.4-13, 1.5-9, 1.6-9
2.1-1, 2.2-1, 2.3-5, 2.4-1, 2.4-5, 2.5-3, 2.6-3, 2.7-7
3.1-9, 3.2-3, 3.5-7
4.2-7, 4.3-2
5.1-3, 5.1-5, 5.2-1
6.1-5, 6.2-3
8.1-3, 8.2-5

Final exam:

There will be no books, notes, or calculators allowed for the final exam. A sheet will be provided containing facts about the binomial, geometric, Poisson, exponential, and normal distributions. Specifically, formulas will be given for the probability mass or density function, the mean, and the variance for each of these distributions. You can see this sheet here, in postscript or PDF. You will also be provided with whatever tables from the back of the book you will need (eg, the tables for the normal and Possion distributions). The exam will be on all the material that has been covered, including the sections of the textbook listed above, and the general ideas that were described in the assignment handouts (eg, the idea of causal networks). There will be some questions that require writing simple R functions, but marks will not be taken off for minor misunderstandings of R.

Mid-term test:

Here are the answers: Postscript, PDF


Assignment 1, due Nov. 3: Postscript, PDF.
Solution to Part I: Postscript, PDF.
Solution to Part II: R program, output of, output of spam.probability.

Assignment 2, due Nov. 24: Postscript, PDF.
Here is the mtf.lookup function and examples of its use.
Here are some R facilities needed for this assignment.
Solution to Part I: Postscript, PDF.
Solution to Part II: R program, output, plots in postscript, discussion.

Assignment 3, due Dec. 5: Postscript, PDF.
Solution: Postscript, PDF, R program, output of R program.

Extra things:

The Monty Hall puzzle and the R program to simulate it. The program is also available on CQUEST (see the CQUEST page).

Another probability puzzle for you to contemplate.

Here is the script of the R demo from the October 17 lecture.

An R program that solves Exercise 2.5-3.

An R program that simulates a queue, and also figures out state probabilities using matrix operations.