Week 1 — Probability, Sampling, and the Logic of Inference

Rebuild probability and frequentist inference from the ground up, using simulation as the microscope, so OLS in Week 2 rests on solid foundations. See ../../TOC.md for the full plan.

Chapters

Notebooks (`../../../notebooks/week-01/`)

nb1.1 LIE/LTV by simulation · nb1.2 Covariance matrices & correlation heatmaps · nb1.3 Sampling-distribution explorer · nb1.4 LLN/CLT convergence · nb1.5 Power curves & the t-test from scratch
All verified to run headless (matplotlib Agg backend, seeded default_rng(42)).

Problem sets (solutions in Appendix E)

PS 1.1 Conditional probability & LIE/LTV · PS 1.2 Expectation/variance/covariance geometry · PS 1.3 Bias/variance/MSE · PS 1.4 CLT/LLN simulation · PS 1.5 Power, size, CIs

Lab, mentor, assessment

Lab 1 — Build a Coin-Flip Universe
Mentor Session 1 — “What is a finding?” (anchored to Gao, Han, Li & Zhou 2018, JFE)
Week 1 Assessment + Rubric

# Week 1 — Probability, Sampling, and the Logic of Inference

Rebuild probability and frequentist inference from the ground up, using simulation as the
microscope, so OLS in Week 2 rests on solid foundations. See [`../../TOC.md`](../../TOC.md) for the
full plan.

## Chapters
1. [Ch 1.1 — Joint, Conditional, and the Two Laws That Run Everything](ch11-joint-conditional-two-laws.md) (LIE, LTV)
2. [Ch 1.2 — Expectations, Variance, Covariance as Geometry](ch12-expectation-variance-geometry.md)
3. [Ch 1.3 — Estimators and Their Sampling Distributions](ch13-estimators-sampling-distributions.md)
4. [Ch 1.4 — The LLN and the CLT, Shown Not Asserted](ch14-lln-clt.md)
5. [Ch 1.5 — Hypothesis Testing Done Right](ch15-hypothesis-testing.md)

## Notebooks (`../../../notebooks/week-01/`)
- nb1.1 LIE/LTV by simulation · nb1.2 Covariance matrices & correlation heatmaps · nb1.3 Sampling-distribution explorer · nb1.4 LLN/CLT convergence · nb1.5 Power curves & the t-test from scratch
- All verified to run headless (`matplotlib` Agg backend, seeded `default_rng(42)`).

## Problem sets (solutions in [Appendix E](../../appendices/E-solutions-manual/))
- [PS 1.1](ps1.1.md) Conditional probability & LIE/LTV · [PS 1.2](ps1.2.md) Expectation/variance/covariance geometry · [PS 1.3](ps1.3.md) Bias/variance/MSE · [PS 1.4](ps1.4.md) CLT/LLN simulation · [PS 1.5](ps1.5.md) Power, size, CIs

## Lab, mentor, assessment
- [Lab 1 — Build a Coin-Flip Universe](lab1-coin-flip-universe.md)
- [Mentor Session 1 — "What is a finding?"](mentor1-what-is-a-finding.md) (anchored to Gao, Han, Li & Zhou 2018, *JFE*)
- [Week 1 Assessment + Rubric](assessment1.md)