MATH 302 - Introduction to Probability (Winter term 2, 2015)

Lectures: Mon Wed Fri 11:00 - 12:00
LSK 201
Instructor: Eric Fusy
fusy ∞
Office hours: Mon 15:00-16:30 Fri 13:30-15:00 in LSK300B
Discussion board: On Piazza (access here)
Textbook: "Introduction to probability" (2nd revised edition) by Grinstead and Snell, can be found at the bookstore and electronically here
Course Outline: You can find a course syllabus here.
  1. Sample spaces, events, axioms of probability
  2. Some elementary combinatorics. Combinations and permutations
  3. Conditional probabilities, independence and Bayes Formula
  4. Discrete random variables, expectation and variance
  5. Continuous probability densities, continuous random variables, expectation and variance
  6. Joint distributions, marginal distributions and conditional distributions
  7. Sums of random variables, generating functions for random variables
  8. Limit Theorems: weak law of large numbers, central limit theorem
Summary: Here is a file (updated every week) summarizing what we have seen, with pointers to the textbook.
Evaluation: 15% homework (single lowest mark is dropped)
35% midterm in class, on Wed. February 24th;
50% final exam, April 16th at 8:30am.
Policy on missed course work is in the syllabus.
Midterm The midterm was in class, Wednesday Feb. 24th from 11:00am to 11:50am. Covered textbook sections for midterm: 1.2, 3.1, 3.2, 4.1, 5.1 (without hypergeometric and Benford), 6.1, 6.2, and Theorem 8.1 from 8.1.

Here is the sample midterm with its solution: problems   solution

Here is the midterm with its solution: problems   formula sheet   solution
Final The final will be in BUCH A101 Saturday April 16th from 8:30am to 11:00am. It covers everything that has been seen in class (see summary file above) since beginning of term (including the period before midterm), except derangements, gambler's ruin, Poisson process, and moment generating functions.

In the Grinstead and Snell textbook, material to be known for final corresponds to all of Chapters 1-9 except for the following parts that are optional reading: - discussions on computer simulations and programming, historical remarks - discussion from p.80 (Factorials) to p.88 in 3.1 - Hypothesis testing, inclusion-exclusion and hat-check problem in 3.2 - card shuffling (3.3) - paradoxes (4.3) - everything about hypergeometric, Benford, Maxwell, Rayleigh, Cauchy, chi-squared random variables (in chapter 5 and subsequent chapters) - martingales and stock prices (in 6.1) - queues (in 6.3 p.275) - Monte Carlo method in 8.2 - discussion from p.344 to p.352 in 9.2

In Ross textbook (8th edition) the sections corresponding to what is to be known for final are: - Chap.1: 1.1 to 1.4 - Chap.2: 2.1 to 2.5 - Chap.3: 3.1 to 3.4 - all of Chap.4 except 4.8.2, 4.8.3, 4.8.4 - all of Chap.5 except 5.5.1, 5.6.2, 5.6.3, 5.6.4 - Chap.6: 6.1 to 6.5 - Chap.7: 7.3 (just formula 3.1), 7.4 and 7.5 - Chap.8: 8.1 to 8.3

Here is a set of exercises to practice (restricted to what has been seen after midterm): problems   solution   rules of conduct    formula sheet