statistics

How to read a clinical trial result with discipline — the difference between absolute and relative risk reduction, what number-needed-to-treat captures, what confidence intervals actually mean, the hierarchy of evidence quality, and why statistical significance is not the same as clinical importance.

Build the vocabulary that underlies all of ML: sample spaces, discrete and continuous random variables, PMFs, PDFs, and CDFs. Then tour the key distributions — Bernoulli, Binomial, Categorical, Gaussian, Poisson, Exponential, Uniform — with their parameters, mean, variance, and exactly when each appears in practice.

Master the three numbers that summarize any distribution: mean, variance, and standard deviation. Derive linearity of expectation, understand covariance and correlation, then see why the Central Limit Theorem makes the Gaussian unavoidable — with a worked numeric example from scratch.

From raw data to defensible conclusions: derive Maximum Likelihood Estimators for Bernoulli and Gaussian, understand bias-variance in estimation, construct confidence intervals, and learn what p-values actually say — and don't say — including the most common misinterpretation that has corrupted thousands of papers.

Understand what it really means to update beliefs with data. Derive Bayes' theorem from first principles, dissect the roles of prior, likelihood, posterior, and evidence, work through a complete Beta-Binomial conjugate example numerically, and see why the base-rate fallacy trips up even experts.