Probabilities

This course will introduce probability spaces, the concepts of probability and independence, and will define discrete and continuous random variables, with an emphasis on modeling.

Probability spaces.

Random experiments. Events. Parallels between probability theory and set theory. Populations. Probabilities.

ProbabilityConditional Probabilities and Independence

Conditional probability; total probability formula; Bayes' theorem. Independence of events; Poincaré's formula.

Discreterandom variables.

Definition of a random variable. Probability distribution. Cumulative distribution function. Moments. Functions of a random variable. Common discrete distributions: uniform, Bernoulli, binomial, hypergeometric, geometric, and Poisson.

Random variables with the following density functions:

Distribution function, density. Moments. Functions of a random variable. Distributions defined by a standard density: uniform, exponential, and normal distributions.

The first-year analysis courses (HAX103X and HAX201X) and  

HAX101X – Reasoning and Set Theory

HAX203X – Arithmetic and Counting

Recommended prerequisites: First-year math

Hourly volumes:

            CM: 24

            TD: 25.5

            Practical Work:

            Lot: