Introducing the concept of the probability of an event. Also covers set operations and the sample-point method.
Introducing conditional probability and independence of events. Bayes' rule comes in as well.
The probability mass function, cumulative distribution function, expectation and variance for random variables.
We introduce the binomial (Bernoulli), geometric and Poisson probability distributions and their properties. The properties include their expectations, variances and moment generating functions.
The probability density function, cumulative distribution function, expectation and variance for a continuous random variable.
The uniform distribution, normal distribution, exponential distribution and their properties.
Joint probability distributions of two or more random variables defined on the same sample space. Also covers independence, conditional expectation and total expectation.
Finding the distribution of a real-valued function of multiple random variables. There's the method of distribution functions, transformations and moment generating functions.
We observe a random sample from a probability distribution of interest and want to estimate its properties. The CLT also comes into place.
A brief review of probability theory and statistics we've learnt so far.