STATS 2D03 — Introduction to Probability

McMaster University · Fall 2024

About These Notes

Tutorial notes written by Anna Ly for STATS 2D03 during the Fall 2024 semester. They were double-checked by Hyuna Seo and Abhiroop Chowdhury — Hyuna also picked the questions.

The instructors were Katherine Davies and J. E. Paguyo. We followed A First Course in Probability by Sheldon Ross, 10th edition.

The textbook has a higher emphasis on word problems. If you are interested in pursuing statistics and mathematics, I would highly recommend Probability and Statistical Inference by Hogg, Tanis, and Zimmerman instead, which focuses more heavily on mathematics.

Questions in tutorials were from the textbook, except Tutorial 7 which Hyuna came up with. Moment generating functions and the convolution transformation method were covered in the course, but there were no tutorials covering those parts.

Tutorial Notes

Tutorial 1
Topic: Elementary counting problems.
Tutorial 2
Topics: Sample spaces, probability.
Tutorial 3
Topic: Conditional probability.
Tutorial 4
Topic: Probability mass functions.
Tutorial 5
Topics: Discrete cumulative distribution functions and expected values.
Tutorial 6
Topics: Total law of probability, Poisson approximation to binomial.
Tutorial 7
Topics: Discrete probability distributions — binomial, geometric, hypergeometric, negative binomial.
Tutorial 8
Topic: Probability density function.
Tutorial 9
Topics: Standard normal distribution, binomial approximation to normal.
Tutorial 10
Topics: Univariate transformations, bivariate probability distributions.
Tutorial 11
Topics: Sum of two probability distributions (not using moment generating functions).