What you'll learn

40 lessons in Probability

Discrete probabilityConditional probabilityRandom variables & expectationContinuous distributionsJoint distributions & independenceVariance & covarianceCentral Limit TheoremMarkov chains introDiscrete distributions: Bernoulli, binomial, Poisson, geometricContinuous distributions: exponential, gamma, betaMoment generating functionsLaw of large numbersModes of convergenceConditional expectationMartingalesBrownian motion introProof: linearity of expectationProof: Markov & Chebyshev inequalitiesProof: weak LLN from ChebyshevBayesian inference deeperRandom walksCharacteristic functionsOptional stopping theoremItô calculus (intro)Probability generating functionsBranching processes & extinctionAbsorbing Markov chainsErgodic chains & stationary distributionsGambler's ruinThe Poisson processOrder statisticsConvolutions: sums of independent variablesConcentration inequalitiesLarge deviations & Chernoff boundsCoupling & total variation distanceMarkov chain mixing timesEntropy & information theoryContinuous-time Markov chainsQueueing theory & Little's lawRandom graphs (Erdős–Rényi)

How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Probability exactly where it's useful.

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