30d roadmap · 5 milestones
30-Day Probability & Statistics
Daily (5d/wk): 45m concepts (canonical externals) + 45m problems + 15m notes. Every week ships code or a writeup. External-heavy (Seeing Theory, MIT OCW, StatQuest, ISL). Not aesthetic math — the gym is solving, simulating, checking assumptions.
Outcome: Active probability & statistics — solve, derive, implement. No passive video watching as a substitute for problems.
How to work this roadmap
Treat each milestone as a claim that must be supported by evidence. Before reading, write what you think the mechanism does and where it will fail. After studying the linked concepts, run the drills without copying an answer, preserve the output, and revise the explanation. Move forward when you can connect the milestone goal to a working implementation, benchmark, architecture decision, or reviewable design artifact.
The 30d horizon is a sequencing aid, not a completion badge. Spend more time where your prediction and the observed behavior disagree. Keep a short decision log containing the mechanism selected, alternatives rejected, expected failure mode, measurement used, and remaining uncertainty. Review that log with FSRS prompts so the roadmap produces durable system judgment rather than a temporary tour of terminology.
At the end, explain Active probability & statistics — solve, derive, implement. No passive video watching as a substitute for problems. from first principles to a reader outside the domain. A strong explanation should survive follow-up questions about correctness, cost, latency, resource use, security, recovery, and operational visibility. If it cannot, return to the milestone that contains the missing mechanism and build a smaller falsifiable example.
Milestones
Milestone 1
Prerequisites — unlock the rest of this path
Concepts the later milestones depend on. Without these the planner cannot serve the rest of this roadmap.
Concepts
Milestone 2
Week 1 — Probability
Conditional probability, distributions, expectation — the language of uncertainty.
Concepts
Build evidence
- Simulate coin flips, dice, and random walks — Code simulators (no stats libraries): Bernoulli trials, dice sums, and a 1D random walk. Plot or print distributions and compare sample mean to theory.
- Weekly math writeup (public note) — Explain one concept you drilled this week in your own words — derive or prove one step, include one mistake you caught yourself making.
Milestone 3
Week 2 — Summaries & sampling
Describe data honestly; understand why averages become Normal.
Concepts
- Descriptive Statistics
- Covariance & Correlation
- Sampling & the Central Limit Theorem
- Estimation & Confidence Intervals
Build evidence
- Implement mean, variance, correlation from scratch — On a real CSV (or synthetic data), compute mean, variance, std dev, covariance, and Pearson r without pandas/numpy — loops only.
- Weekly math writeup (public note) — Explain one concept you drilled this week in your own words — derive or prove one step, include one mistake you caught yourself making.
Milestone 4
Week 3 — Inference & experiments
Hypothesis tests, regression, and real A/B practice for SWE.
Concepts
Build evidence
- A/B test analysis report — Analyze a mock or real experiment: check SRM, compute CI on the lift, interpret p-value and practical significance, and write a ship/no-ship recommendation.
- Weekly math writeup (public note) — Explain one concept you drilled this week in your own words — derive or prove one step, include one mistake you caught yourself making.
Milestone 5
Week 4 — Bayesian & likelihood
Posterior thinking and MLE — the bridge to ML loss functions.
Concepts
Build evidence
- Analyze a fake trading signal — Given (or generate) a spurious 'alpha' signal on synthetic or historical noise, show why it fails: multiple testing, in-sample overfit, or non-stationarity.
- Weekly math writeup (public note) — Explain one concept you drilled this week in your own words — derive or prove one step, include one mistake you caught yourself making.