# Random Variable

## 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.