Chapter 1 Hello, World!

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In probability, we solve forwards. It starts with an exact and well-defined rule. We use this rule to predict what will happen in the future. We don’t know the results, but probability allows us to quantify what should happen. In statistics, we solve backwards. It starts with the end results, known as data. We take this data and try to determine what well-defined rules created it.

T Janesky

1.1 Cover

This guide is written from a theoretical perspective, aiming to distill the theories of probability. This work is a reflection of my commitment to sharing the beauty and complexity of statistical sciences. If you appreciate this please star the repository. Should you find any discrepancies, please submit an issue via GitHub. The repository for this book can be found here. Additionally, much of these notes I found easy to write out after reading Fundamentals of Probability, with Stochastic Processes by Saeed Ghahramani.

1.2 Contents

  • Probability of Events
  • Conditional Probability
  • Random Variables & Probability Distributions
  • Special Discrete Distributions
  • Special Continuous Distributions
  • Bivariate Random Variables
  • Estimation