Lectures related to Applied Probability and Stochastic Processes: Tutorial 02

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Covers random walks on a lattice, focusing on return probabilities and their dependence on dimensionality.

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Covers the normal distribution, including its properties and calculations.

Covers the properties of the symmetric random walk in stochastic processes.

Covers stochastic models for communications, focusing on random variables, Markov chains, Poisson processes, and probability calculations.

Covers examples of continuous-time stochastic processes in communications.

Explores the Fokker-Planck and KPZ equations in stochastic processes and random growth models.

Covers the analysis of random walks and their return probabilities in multiple dimensions.

Covers fundamental concepts in probability and statistics, including the law of total probability, Bayes' theorem, and independence of events.

Covers stochastic processes in continuous time, including probability functions and stock processes.

Covers Simpson's paradox, probability distributions, and real-life examples in probability and statistics.

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Explores discrete random variables, mass functions, and distribution functions in probability and statistics.

Covers free fields and probabilistic functions, focusing on random variables and their properties.

Covers the characterization of stochastic processes, focusing on their mathematical foundations and real-world applications.

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.