# Probability and Statistics for Machine Learning and Data Science

This series of blog posts introduces probability and mathematical statistics. While I wrote these posts with a focus on machine learning and data science applications, they are kept sufficiently general for other readers.

Some familiarity with vectors and matrices, as well as differential and integral calculus, is necessary to fully understand all concepts. If these topics are new to you or you need a refresher, I suggest you check out my other series on linear algebra and calculus first.

## Series Overview

### Basic Statistics and Probability

- Introduction to Probability and Random Variables
- Probability Mass Function and Probability Density Function
- Conditional Probability and Independence
- The Law of Total Probability and Bayesian Inference
- Variance and the Expected Value
- Covariance and Correlation
- Bernoulli Random Variables and the Binomial Distribution
- Normal Distribution and Gaussian Random Variables
- Maximum Likelihood Estimation
- Multivariate Gaussian Distribution
- Maximum Likelihood Estimation for Gaussian Distributions
- The Law of Large Numbers
- The Central Limit Theorem
- Confidence Intervals and Z Score

### Probability Distributions

- Factorization Theorem and the Exponential Family
- Poisson Distribution
- Exponential Distribution
- Gamma Distribution
- Beta Distribution
- Conjugate Priors
- Geometric Distribution
- Chi-Square Distribution and Degrees of Freedom
- Student’s T-Distribution

### Statistical Testing

### Critical Value Tables

For your convenience, here are the most important tables for looking up critical values.

For writing these posts I’ve relied on the following books:

**Introduction to Mathematical Statistics** by Hogg, McKean, and Craig**Pattern Recognition and Machine Learning **by Christopher Bishop**The Elements of Statistical Learning** by Trevor Hastie, Robert Tibshirani, et al.**Mathematics for Machine Learning** by Deisenroth, Faisal and Ong**Deep Learning** by Ian Goodfellow, Yoshua Bengio, et al.**Machine Learning: A Probabilistic Perspective** by Kevin Murphy

I’m grateful to the authors for writing these amazing books.