This series contain the notes I've taken for courses STAT 6510 and STAT 6520 -

**Mathematical Statistics I & II**. The text book recommended for this course is*Mathematical Statistics with Applications (7th edition)*by Wackerly, Mendenhall and Sheaffer.Basic Concepts

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

Sep 25, 2019

Statistics

Conditional Probability

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

Sep 26, 2019

Statistics

Bayesian

Definitions for Discrete Random Variables

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

Oct 6, 2019

Statistics

Visualization

Common Distributions of 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.

Oct 7, 2019

Statistics

Visualization

Distribution

Definitions for Continuous Random Variables

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

Oct 9, 2019

Statistics

Common Distributions of Continuous Random Variables

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

Nov 1, 2019

Statistics

Visualization

Distribution

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.

Nov 8, 2019

Statistics

Distribution

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.

Dec 8, 2019

Statistics

Visualization