Carpan Collector ProblemExplores the Carpan collector problem, analyzing expected completion times and waiting times for collecting different objects uniformly at random.
Hoeffding's InequalityExplores Hoeffding's inequality and its applications in probability theory and statistical analysis.
Large Deviations PrincipleExplores the Large Deviations Principle, focusing on exponential tail decay and Laplace transform analysis.
Distribution of Random VariablesIntroduces the concept of the distribution of a random variable and explores specific cases of discrete and continuous random variables.
Conditional Expectation: BasicsIntroduces the basics of conditional expectation, covering definitions, properties, and examples in the context of random variables.
Independence of Sub-FieldsExplores the concept of independence of sub-fields within a field and its implications in random variables.
Optional Stopping TheoremExplores stopping times, the optional stopping theorem, F-measurable random variables, and martingales.
Convolution of Random VariablesExplores the convolution of random variables, discussing sums of independent variables and their distributions in discrete and continuous contexts.
