# Applied Probability Theory from Scratch

## Summary

Recent advances in Machine Learning and Artificial Intelligence have result in a great deal of attention and interest in these two areas of Computer Science and Mathematics. Most of these advances and developments have relied in stochastic and probabilistic models, requiring a deep understanding of Probability Theory and how to apply it to each specific situation

In this lecture we will cover in a hands-on and incremental fashion the theoretical foundations of probability theory and recent applications such as Markov Chains, Bayesian Analysis and A/B testing that are commonly used in practical applications in both industry and academia

## Program

**Basic Definitions and Intuition**Understand what is a probability

Calculate the probability of different outcomes

Generate numbers following a specific probability distribution

Estimate Population sizes from a sample

**Random Walks and Markov Chains**Simulate a random walk in 1D

Understand random walks on networks

Define Markov Chains

Implement PageRank

**Bayesian Statistics**Understand conditional Probabilities

Derive Bayes Theorem

Understand how to Update a Belief

**A/B Testing**Understand Hypothesis Testing

Measure p-values

Compare the likelihood of two outcomes.