Brownian Motion: Fundamentals and Applications

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Introduces the concept of the distribution of a random variable and explores specific cases of discrete and continuous random variables.

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Explores moment-generating functions, linear combinations, and normality of random variables.

Covers properties and transformations of discrete random variables, focusing on PMF and expectation.

Covers random variables, probability functions, expectations, variances, and joint distributions.

Introduces the basics of probability models, covering random variables, distributions, and statistical estimation.

Covers properties and calculations related to the normal distribution, including probabilities and quantiles.

Explores air pollution analysis using wind data, probability distributions, and trajectory models for air quality assessment.

Explores PDFs and CDFs for discrete and continuous random variables, including Gaussian, uniform, and exponential distributions.

Covers the fundamentals of probability theory, including conditional probability, Bayes' rule, and random variables.