# Mathematical Probability

### A mini-course covering mathematical probability

This is an overview of mathematical probability

### Format

- You should visit the sections below in order starting with Section 1.
- Each section below has several videos explaining the listed concepts, and then exercises with videos.

## Mathematical Probability

View Section 1: Probabilistic Models and Probability Laws- Kolmogorov's Axioms
- Discrete Uniform Probability Spaces
- Complement Rule
- Monotonic Property and Inclusion & Exclusion

- Conditional Probability
- Law of Total Probability
- Bayes' Formula
- Independence of Two Events
- Complement of Independent Events Conceptual
- Independence of \(n\) Events
- Bernoulli Trials

- Discrete Random Variable
- Probability Distribution and Probability Mass Function
- Functions of Random Variables
- Cumulative Distribution Function

- Expectation
- Variance and Standard Deviation
- Properties of Expectation and Variance
- Continuous Random Variable and Probability Density Function
- Probability Density Function
- Expectation of Continuous Random Variable
- Uniform Probability Density Function

- Binomial Random Variable
- Indicator Random Variable
- Geometric Random Variable
- Pascal Random Variable
- Negative Binomial Random Variable
- Poisson Random Variable
- Law of Rare Events
- Approximating Binomial Distribution from Poisson
- Poisson Random Variable and Law of Rare Events

- Exponential Random Variable
- Exponential Distribution
- Gaussian Normal Random Variable
- Normal Approximation of the Binomial
- Continuity Correction

- Joint Distribution and Joint PMF
- Marginal PMF
- Joint PMF of Continuous Random Variables
- Joint PDF
- Joint PMF and Marginal PMF
- Uniform Distribution

- Independence of Discrete Random Variables and Continuous Random Variables
- Variance of Sums and Covariance
- Correlation
- Variance of Sums of Random Variables
- Properties of Covariance and the Correlation Coefficient
- Correlation between Indicator of Two Events
- Applications of Indicator Random Variable
- Exchangeable

- Moment Generating Function
- Moment Generating Function for Poisson Random Variable
- Moment Generating Function for Normal Random Variable
- Moment Generating Function for Exponential Random Variable
- Moment
- Moments of Exponential Random Variable
- Moments of Normal Random Variable

- Tail Probability
- Markov’s Inequality
- Chebyshev’s Inequality
- Convergence in Probability
- Weak Law of Large Numbers