Mathematical Statistics

Basic Concepts

Introducing the concept of the probability of an event. Also covers set operations and the sample-point method.

Conditional Probability

Introducing conditional probability and independence of events. Bayes' rule comes in as well.

Definitions for Discrete Random Variables

The probability mass function, cumulative distribution function, expectation and variance for random variables.

Common Discrete 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.

Definitions for Continuous Random Variables

The probability density function, cumulative distribution function, expectation and variance for a continuous random variable.

Common Continuous Random Variables

The uniform distribution, normal distribution, exponential distribution and their properties.

Multivariate Probability Distributions

Joint probability distributions of two or more random variables defined on the same sample space. Also covers independence, conditional expectation and total expectation.

Functions of Random Variables

Finding the distribution of a real-valued function of multiple random variables. There's the method of distribution functions, transformations and moment generating functions.

Sampling Distribution and Limit Theorems

We observe a random sample from a probability distribution of interest and want to estimate its properties. The CLT also comes into place.

Brief Review Before STAT 6520

A brief review of probability theory and statistics we've learnt so far.