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 to STA 247 is STA 248, which will cover statistical inference. Together, STA 247 plus STA 248 are accepted as prerequisites to most higher-level statistics courses (eg, STA 302).

**ANNOUNCEMENTS:** You can collect marked term work on January 25
from 1:10 to 2:00, in SS6026A.

**Instructor:**

Radford Neal,Office:SS6026A,Phone:(416) 978-4970,Email:radford@stat.utoronto.ca,Office hours: Tuesdays, 2:10-3:30, starting September 20, in SS 6026A.

**Prerequisites:** MAT135/137/157, CSC 108/148.
**Exclusions:** ECO227/STA255/STA257

**Lectures:**

Mondays 3:10 to 5:00 and Fridays 3:10 to 4:00, in WB 116, from September 12 to December 6. There is no lecture on October 10 (Thanksgiving) or November 7 (Fall break). There willnotbe a Thanskgiving makeup lecture on December 7.Stat aid centre hours: Thursdays 11:00 to 12:30, in SS 1091.

**Evaluation:**

24% Four in-class quizes (6% each)

31% Four assignments (worth 6%, 9%, 9%, 7%)

45% Final exam, scheduled by the Faculty

All assignments are to be done by each student individually.

Requests for assignments or quizes to be remarked must be made in writing to the instructor (not the TAs) within one month of the work being returned.

**Accomodating illness and other special circumstances:**

If due to illness or other serious personal difficulties, you are unable to complete an assignment on time, or unable to write one of the quizes, you should contact the instructoras soon as possible. For quizes, accomodation will be by taking that portion of the mark from other work. For assignments, you may be allowed to hand in the assignment up to one week late; if that is not possible, that portion of the mark will be taken from other work.Note that for the final exam, accomodation for illness or other difficulties is handled officially through your college/faculty, not by the instructor.

**Computing:**

Parts of the assignments will involve writing programs in the R language. You can download R for free there for your own computer, and look at documentation, including an Introduction to R.You can also use R on the CQUEST computer system for this; you should be able to request an account here. CQUEST can be accessed from various locations on campus, or from home.

**Textbook:**

There is no paper text for this course. I will be posting lecture summaries, and will sometimes refer to sections of the following on-line books:Introduction to Probability and Statistics Using R, G. Jay Kerns.

A PDF of the version I will refer to, with added annotations (errata) by myself, is here.You can also get just individual chapters (with annotations) related to the course below:

Chapter 2: Introduction to RIntroduction to Probability, Charles M. Grinstead and J. Laurie Snell.

The PDF of the version I will refer to is here.

Quiz 1 with answers. Quiz marks will be adjusted from the mark m on the quiz paper to 100-(100-m)^{2}/100. For example, 50 is adjusted to 75.Quiz 2. Marks will be adjusted in the same way as for Quiz 1.

Quiz 3. Marks will be adjusted in the same way as for Quiz 1.

Quiz 4. Marks will be adjusted from the mark m on the quiz paper to 100-100(1-m/100)

^{1.5}.

Assignment 1: handout. Due in class on October 7. Clarification: In question 2, when it says that events

A,B,C, andDare independent, it is meant that they are mutually independent. An explanation of mutual independence has been added to the end of the week3 lecture notes below. Here are the solutions.Assignment 2: handout. Due in class on October 28. Here are the solutions. Note: In the program for the solution to Question 3, the call

b<-sample(0:5,prob=B.given.A.table[a,])should beb<-sample(0:5,1,prob=B.given.A.table[a,]). The program actually works anyway! (But the effect of the random seed selection is different.)Assignment 3: handout, R hints. Due in class on November 21.

Assignment 4: handout. Due in class on December 5. Solution: program, output.

**Final Exam:**

Time and place scheduled by the Faculty of Arts and Science - see here. Note that there are two locations, with division by student name.There will be no books, notes, or calculators allowed for the final exam. A sheet will be provided containing facts about some standard distributions. You can see this sheet here. The exam will be on all the material that has been covered. You may need to write simple R commands, such as in Question 2 of Assigment 2, but marks will not be taken off for minor misunderstandings of R.

Here are the old final exams from 2004 and 2006.

Marks on the final exam will be adjusted from the mark m on the paper to 100-(100-m)

^{2}/100. For example, 50 is adjusted to 75.

Practice problem set 1: problems, answers.

Practice problem set 2: problems, answers.

Week Monday Friday Lecture lectures lectures summaries Sep 12: intro: probability, more on R and week1 applications, and R, probability probability basics 19: conditional prob, independence, week2 interpretations, A1 handed out counting 26: Bayes' rule, odds, Quiz 1 week3 when to consider outcomes equally likely, R function Oct 3: random variables, joint distributions, week4 expectation independence of r.v. A1 due 10: ----- binomial distribution, week5 simulation, A2 handed out 17: variance, properties of Quiz 2 week6 expectation and variance, Chebyshev's inequality 24: i.i.d. random variables, graphical models, week7 law of large numbers A2 due 31: geometric distribution, cumulative dist fns, week8 continuous random vars, uniform distribution probability density fns A3 out Nov 7: ----- Quiz 3 ----- 14: exponential distributions, Mixture distributions week10 normal distributions, Central Limit Theorem 21: Bayes' Rule when random Quiz 4 week11 variables are continuous, Markov chains A3 due 28: Markov chains and Poisson distribution week12 matrices, equilibrium distribution A4 out Dec 5: Formulas for variance, ---- week13 brief intro to statistical inference, application A4 due Final exam scheduled by the Faculty

2003

2004

2006