From uncertainty about individual outcomes to evidence about population means — and onward to regression.
How to read · 三条阅读路线
Complete learning: 00 concept map → 01–12, including examples and derivations → 14 exercises → 15 empirical workflows. Read 13 as an optional extension.
Probability refresh: 00 → 01–06 → 08 for the bridge to inference. Keep the population distribution and sampling distribution distinct.
Exam review: 00 tricky boundaries → 16 formula sheet → attempt 14 without solutions → revisit the linked derivations.
Table of contents
Overall Concepts List
Core jargon, examples, implication ladders, and tricky boundaries
01 / COREProbability Distributions
Outcomes, PMF, CDF, density, and quantiles
02 / COREExpectation, Moments & Shape
Means, variance, transformations, and distribution shape
03 / COREConditional Information & Prediction
Joint distributions, iterated expectations, and best prediction
04 / COREDependence & Covariance Algebra
Independence, correlation, weighted sums, and diversification
05 / CORENormal, χ², t & F
Distribution constructions and exact probability calculations
06 / CORESampling, LLN & CLT
Sampling distributions, concentration, and normal approximation
07 / COREEstimators & Least Squares
Bias, consistency, efficiency, BLUE, and optimization
08 / COREVariance Estimation & Standard Errors
Degrees of freedom, continuous mapping, and studentization
09 / CORETests & Confidence Intervals
p-values, size, power, coverage, and precision
10 / COREComparisons & Causal Effects
Independent groups, pairs, experiments, and selection
11 / CORESmall Samples & Student t
Exact inference, pooled variance, and unequal variances
12 / CORECorrelation → Regression
Sample moments, OLS, exogeneity, and asymptotic reasoning
13 / COMPANIONBootstrap & Paper Connections
Resampling, limits, List, Efron, and Jansson research
14 / COMPANIONIntegrated Exercises & Solutions
Nineteen problems connecting calculations and reasoning
15 / COMPANIONEmpirical Workflows
Joint tables, CPS earnings, experiments, and Monte Carlo
16 / COMPANIONNotation & Formula Reference
Conditions, formulas, and mistakes to avoid
17 / COMPANIONSources & Coverage Map
Section-level traceability and editorial corrections
Reading contract · 内容与范围
All main sections and appendices have been mapped to these modules. Repeated explanations and numerical drills are consolidated; distinct reasoning chains remain. Original datasets are not required to understand the text. Where the textbook asks for external data, a complete workflow is supplied and uncomputed results are not invented.
The notes explicitly separate exact results, asymptotic approximations, and extensions. For original-page traceability or corrections to extracted formulas, open Sources & Coverage Map.