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Poisson processesCovers the properties and construction of Poisson processes from i.i.d. Exp(X) random variables, emphasizing the importance of the process rate and jump time distributions.
Random Walks on Discrete SpacesExplores random walks on discrete spaces and their properties, including multivariate random variables and Poisson distributions.
Stochastic Models for CommunicationsExplores stochastic models for communications, covering mean, variance, characteristic functions, inequalities, various discrete and continuous random variables, and properties of different distributions.
Review of ProbabilityCovers the review of probability concepts including Poisson distribution and moment generating functions.
Poisson Process: PropertiesCovers the properties of Poisson processes, including arrival times and stochastic models for communications.
Insurance Risk ModelingCovers the modeling of insurance risk, discussing joint distributions and the impact of accidents.
Probability and StatisticsCovers Simpson's paradox, probability distributions, and real-life examples in probability and statistics.
Partitioning EquilibriumCovers partitioning equilibrium, sorption isotherms, and the role of natural organic matter in environmental chemistry.
Discrete Random VariablesCovers properties and transformations of discrete random variables, focusing on PMF and expectation.
Probability and StatisticsCovers fundamental concepts in probability and statistics, including distributions, properties, and expectations of random variables.
Probability InequalitiesExplores probability inequalities, convergence types, and moment generating functions for distribution approximation.