Advanced Probability: SummaryCovers random variables, sample spaces, probability distributions, functions, expected value, variance, and estimations.
Linearity of ExpectationsCovers the proof of the linearity of expectations for independent random variables and discusses properties of expected value.
Theorem of the AverageExplores the Theorem of the Average, integrability criteria, properties of the integral, and volume concepts.
Probabilités discrètesCovers the basics of discrete probability, including notations, axioms, pmf, examples, expectation, variance, and indicator variables.
Probability and StatisticsCovers moments, variance, and expected values in probability and statistics, including the distribution of tokens in a product.