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Probability ReviewIntroduces subgaussian and subexponential random variables, conditional expectation, and Orlicz norms.
Importance Sampling: Change of VariableExplores importance sampling through a change of variable to speed up Monte Carlo calculations and discusses the impact on stochastic estimates and variance scaling.
Continuous Random VariablesCovers continuous random variables, probability density functions, and distributions, with practical examples.
Continuous Random VariablesExplores continuous random variables, density functions, joint variables, independence, and conditional densities.
Probabilités discrètesCovers the basics of discrete probability, including notations, axioms, pmf, examples, expectation, variance, and indicator variables.
Hypothesis Testing in StatisticsExplores hypothesis testing in statistics, focusing on decision-making based on sample data and controlling error probabilities.
Conditional Expectation: BasicsIntroduces the basics of conditional expectation, covering definitions, properties, and examples in the context of random variables.