Probability and Statistics

reading · we frame, you read MIT or the canonical taught · we author, no canonical fits ↺ spirals back to earlier lessons

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reading · 35 min + ~267 min canonical

Probability: The Language of Uncertainty (and Bayes' Theorem)

Everything you've learned in this ML-math year so far has been about certainty. Linear algebra transforms a vector into another vector — deterministically, exactly. Calculus compu…

primary Harvard Stat 110: Probability (YouTube)

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reading · 35 min + ~267 min canonical L1

Random Variables and Distributions: The Shapes of Uncertainty

The last lesson gave you probability as reasoning — axioms, conditioning, Bayes. This lesson gives it quantitative form. A random variable is the bridge from "events" to "numbers"…

primary Harvard Stat 110: Probability (YouTube)

after L1 locked

reading · 35 min + ~267 min canonical L1

Expectation, Variance, and the Theorems That Make Statistics Possible

A distribution (last lesson) is the full shape of a random variable's uncertainty — but often you don't want the full shape; you want a couple of summary numbers that capture its …

primary Harvard Stat 110: Probability (YouTube)

after L2 locked

reading · 40 min + ~267 min canonical L1

Estimation: MLE, MAP, and Bayesian Inference

The last three lessons were probability — reasoning forward from known distributions. This lesson is where it becomes statistics, and then becomes machine learning: you have data,…

primary Harvard Stat 110: Probability (YouTube)

after L3 locked

reading · 35 min + ~267 min canonical L1

Information Theory: Entropy, Cross-Entropy, and KL Divergence

There's one more mathematical language woven through machine learning, and it comes from a surprising place: the 1948 theory of communication — how to send messages over a noisy w…

primary Harvard Stat 110: Probability (YouTube)

after L4 locked

exercise reading · 15 min L1

Exercises: Easy (Warm-up)

- [ ] Compute Bayes' theorem: medical test with 1% prevalence, 95% sensitivity, 90% specificity — What is P(disease|positive)? - [ ] Simulate the Central Limit Theorem in Python —…

after L5 locked

exercise reading · 30 min L1

Exercises: Medium (Core)

- [ ] Implement Naive Bayes classifier from scratch in Python — Train on text, predict sentiment - [ ] Compute KL divergence between two distributions in Python — Measure how one …

after L6 locked

exercise reading · 45 min L1

Exercises: Hard (Stretch)

- [ ] Implement Bayesian linear regression in Python — Prior on weights, posterior update, compare with MLE - [ ] Implement Markov Chain Monte Carlo (Metropolis-Hastings) in Pytho…

after L7 locked

exercise reading · 60 min L1

Mini-Project

- [ ] Build a spam classifier using Bayesian methods in Python — Tokenize emails, compute class priors and word likelihoods, Laplace smoothing, classify new emails, evaluate with …

after L8 locked

L10

project reading · 360 min L1

Project: Statistical Testing Framework

Build a Python library implementing: confidence intervals (z and t), hypothesis testing (one-sample t, two-sample t, chi-squared), and bootstrap resampling. Apply to a real datase…

after L9 locked

L11

project reading · 300 min L1

Project: Bayesian Inference Engine

Implement Bayes' theorem computation for discrete and continuous (grid approximation) priors. Demonstrate with: medical diagnosis (sensitivity/specificity), spam filtering (Naive …

after L10 locked

L12

assessment reading · 63 min L1

Self-Assessment: Probability and Statistics

- [ ] What is Bayes' theorem? Give an intuitive example (e.g., medical testing). - [ ] What is the difference between MLE and MAP estimation? - [ ] Explain the Central Limit Theor…

after L11 locked

L13

assessment reading · 60 min L1

Quarter 13 Gate Check: Mathematics for ML

- [ ] Course 13.1 knowledge check passed - [ ] Course 13.2 knowledge check passed - [ ] Course 13.3 knowledge check passed - [ ] Neural Network from Scratch capstone completed

after L12 locked

13 lessons. Read in order; spiral back when you need to. By the end you'll have used the core ideas twice — once on the abstract, once on something you'll meet at work next week.