In Part I of this series, we cover basic statistical inference and experimentation, focusing on:

• basic statistics;
• derivation and review of key distributions and their relations;
• hypothesis testing, including an in depth power analysis for the chi-squared statistic;
• experimentation, including A/B tests, stratification, one- and two-factor experiments, and an introduction to bandit algorithms;
• maximum likelihood;
• gradient descent;
• introduction to survival analysis and stochastic processes, including empirical estimation of online survival and event processes.

The theory is illustrated with simulations in Python throughout the text.