STATISTICAL MODELS FOR DATA SCIENCE

Prerequisites & course information

Requisites: Declared in Data Science MS or Data Engineering MS Course Designation: Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Describe the foundations of probability theory, including: the axioms of probability, the concepts of sample space and probability measure, events and their probabilities, and the notions of conditional probabilityand independence Audience: Graduate 2. Explain the concepts of random variables and probability distributions, and calculate or otherwise utilize key mathematical objects and results related to them, including: random number generation, expected values and moments, moment-based probabilistic inequalities, moment generating functions, joint probability distributions of multiple random variables Audience: Graduate 3. Identify the most important probability distributions used in Statistics, cite their properties, create computer visualizations of them, and simulate random variates from these distributions. This includes the normal distribution, the binomial distribution, the exponential distribution, the Poisson distribution, and more Audience: Graduate 4. Apply, and explain the significance of, key results related to the limits of sequences of random variables, including laws of large numbers, the Central Limit Theorem, and the delta method Audience: Graduate 5. Grasp important elements of sampling theory, including: random samples and how to generate them; statistics, such as the sample mean and sample variance, and how to derive or simulate their sampling distributions; and the distributions that arise from a normal random sample, namely the chi-square,T, and F distributions. Audience: Graduate Learning Outcomes: 1. Describe the foundations of probability theory, including: the axioms of probability, the concepts of sample space and probability measure, events and their probabilities, and the notions of conditional probabilityand independence Audience: Graduate 2. Explain the concepts of random variables and probability distributions, and calculate or otherwise utilize key mathematical objects and results related to them, including: random number generation, expected values and moments, moment-based probabilistic inequalities, moment generating functions, joint probability distributions of multiple random variables Audience: Graduate 3. Identify the most important probability distributions used in Statistics, cite their properties, create computer visualizations of them, and simulate random variates from these distributions. This includes the normal distribution, the binomial distribution, the exponential distribution, the Poisson distribution, and more Audience: Graduate 4. Apply, and explain the significance of, key results related to the limits of sequences of random variables, including laws of large numbers, the Central Limit Theorem, and the delta method Audience: Graduate 5. Grasp important elements of sampling theory, including: random samples and how to generate them; statistics, such as the sample mean and sample variance, and how to derive or simulate their sampling distributions; and the distributions that arise from a normal random sample, namely the chi-square,T, and F distributions. Audience: Graduate