This course provides a comprehensive overview of probability theory and statistical inference, covering joint probability distributions, independence, and conditional distributions. Students will explore expected values, variances, and key statistical theorems, including the central limit theorem. Hypothesis testing, regression analysis, and stochastic processes such as Poisson processes and Markov chains will also be examined. Through practical applications and problem-solving, participants will gain essential skills in data analysis and interpretation.

This module presents the joint distributions of multiple random variables, both discrete and continuous and introduces the concept of independence.

This module focuses on the expectation of a random variable and joint random variable. Students will solve problems using the linearity of expectation and identify when its application is inappropriate. We will also explore variance, covariance, and correlation.

This module will apply several limit theorems to solve problems to include the central limit theorem, the Markov inequality, and the Chebyshev inequality. We will also prove Murphy’s Law.

This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.

This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.