INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS I

Prerequisites & course information

Requisites: MATH 234 , 376 , or concurrent enrollment. Not open to students with credit for STAT/MATH 431 or STAT 311 Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall the definitions of fundamental objects and concepts underlying probability theory (e.g. sample spaces and events, the axioms of probability, the notions of conditional probability and independence, random variables and their probability distributions, mathematical expectation, and the joint distribution of one or more random variables) and demonstrate understanding of their properties Audience: Undergraduate 2. Perform important operations in probability (e.g. calculate the probabilities of events, derive the probability distributions of random variables, compute moments and the expectation of functions of random variables, calculate covariances and correlations, and obtain conditional distributions and conditional expectations) and interpret the results Audience: Undergraduate 3. Explain the meaning of key results in probability theory that are especially important in mathematical statistics (e.g. Bayes’ Theorem, probabilistic tail inequalities such as Markov’s and Chebyshev’s inequalities, the Law of Large Numbers, and the Central Limit Theorem) Audience: Undergraduate 4. Identify, utilize, and understand the key properties of, probability distributions that are especially important in statistics, including discrete families of distributions (e.g. the binomial, Poisson, geometric, and negative binomial distributions) and continuous families of distributions (e.g. the uniform, exponential, gamma, and normal distributions) Audience: Undergraduate Learning Outcomes: 1. Recall the definitions of fundamental objects and concepts underlying probability theory (e.g. sample spaces and events, the axioms of probability, the notions of conditional probability and independence, random variables and their probability distributions, mathematical expectation, and the joint distribution of one or more random variables) and demonstrate understanding of their properties Audience: Undergraduate 2. Perform important operations in probability (e.g. calculate the probabilities of events, derive the probability distributions of random variables, compute moments and the expectation of functions of random variables, calculate covariances and correlations, and obtain conditional distributions and conditional expectations) and interpret the results Audience: Undergraduate 3. Explain the meaning of key results in probability theory that are especially important in mathematical statistics (e.g. Bayes’ Theorem, probabilistic tail inequalities such as Markov’s and Chebyshev’s inequalities, the Law of Large Numbers, and the Central Limit Theorem) Audience: Undergraduate 4. Identify, utilize, and understand the key properties of, probability distributions that are especially important in statistics, including discrete families of distributions (e.g. the binomial, Poisson, geometric, and negative binomial distributions) and continuous families of distributions (e.g. the uniform, exponential, gamma, and normal distributions) Audience: Undergraduate