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05
Probability II: Advanced
Continuous distributions, expectation techniques, stochastic processes, martingales, and decision theory.
The first two lessons are free to read. Membership unlocks the full course and tracks your progress.
Become a Member01Continuous Distributions
The Uniform Distribution and Geometric ProbabilityFreeThe Normal DistributionFree
The Exponential Distribution and MemorylessnessMembers
The Gamma and Beta DistributionsMembers
The Multivariate Normal Distribution and Covariance MatricesMembers
The Central Limit TheoremMembers
02Expectation Techniques
Linearity of ExpectationMembers
Indicator VariablesMembers
Symmetry ArgumentsMembers
Conditional Expectation and the Tower PropertyMembers
The Law of the Unconscious StatisticianMembers
03Moments and Inequalities
Moment Generating FunctionsMembers
Probability Inequalities: Markov, Chebyshev, and ChernoffMembers
04Order Statistics
Distributions of Maxima and MinimaMembers
Expected Values of ExtremesMembers
05Stochastic Processes
First-Step AnalysisMembers
Expected Waiting Times for PatternsMembers
Introduction to Markov ChainsMembers
The Poisson ProcessMembers
The Coupon Collector ProblemMembers
Monte Carlo SimulationMembers
06Martingales and Ruin
Fair Games and MartingalesMembers
Gambler's RuinMembers
Optional StoppingMembers
07Decision Theory
Sequential Decision ProblemsMembers
Optimal StoppingMembers
Risk Preferences and UtilityMembers
The Kelly CriterionMembers