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Probability & statistics
Honest reasoning under uncertainty.
You can't know whether the coin lands heads — but you can know exactly how often it will in the long run. Probability quantifies uncertainty; statistics reads evidence backwards from data to truth. Together they're the mathematics of not being fooled.
Your progress
13 lessons
The big ideas
Randomness has structure
A single die roll is unpredictable; a million rolls are astonishingly predictable. Probability is the study of that long-run order — and distributions are its vocabulary.
The normal curve keeps showing up
Add up many small independent influences — measurement errors, genetics, luck — and a bell curve emerges, almost no matter what. That's the central limit theorem, and it's why the bell is everywhere.
Evidence updates belief
Data never proves alone — it shifts belief between explanations. Bayes' theorem makes the update exact, and likelihood turns it into estimation: the engine of fitting any model.
Learning from data is statistics at scale
Generalization is the sampling problem; training is maximum likelihood; overfitting is the bias–variance trade-off. Machine learning is applied statistics with a bigger computer.
The course — start at lesson one
- 01Why statistics mattersReasoning under uncertainty, and why intuition fails.Easy
- 02Data, populations & samplesWhat you measured vs what you care about — and sampling bias.Easy
- 03Center, spread & honest summariesMean vs median, σ, and summaries that don't lie.Easy
- 04Shape, percentiles & spreadQuartiles, IQR, box plots, and reading skew from figures.Easy
- 05Thinking in probabilityLong-run frequencies, combining rules, expected value.Medium
- 06Random variables & distributionsBernoulli to Normal; expectation and variance.Medium
- 07The bell curveWhy bells appear everywhere, and the 68–95–99.7 ruler.Medium
- 08Conditional probability & BayesUpdating belief with evidence — and the base-rate trap.Medium
- 09Sampling & evidenceHow 1,000 people speak for millions — and p-values, demystified.Medium
- 10Estimation, likelihood & MLEBest guesses justified; confidence intervals; Type I/II errors.Hard
- 11Correlation & regressionCovariance, least-squares lines, residuals, and causation.Hard
- 12Statistics for machine learningGeneralization, overfitting, evaluation — where it all converges.Hard
- 13Noise, averaging & SNRStatistics meets signals: fighting randomness with √n.Hard
Out in the world
Machine learning & data science
Estimation, distributions, likelihood, and evaluation are the statistical backbone of every model — from regression to neural networks.
Medical trials & A/B tests
Whether a drug or a feature works is a statistics question: separating real effect from lucky samples via hypothesis testing.
Risk, forecasting & inference
Insurance premiums, demand forecasts, and quality control are expected values and distributions, applied at industrial scale.
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