Document Type
Syllabus
Publication Date
Fall 9-1-2024
Course Description
Probability, a subject that is over two hundred years old, was originally conceived by Pascal and Fermat (circa 1654) to analyze games of chance and has developed into a broadly useful discipline with great charm and deep connections to other branches of mathematics. It is rich in theory and applications and serves as a background for the study of many courses (such as statistics, statistical physics, industrial engineering, communication engineering, genetics, statistical psychology, operational research, and econometrics), in which probabilistic ideas and techniques are employed. The object of Math 441 is to introduce the concepts and methods of probability, and thereby provide the mathematical framework for analyzing probabilities. The stress is on fundamentals that are illustrated with many examples and problems. Philosophically speaking, probability is a description of our uncertainty about the world. Random events influence all aspects of human activities, from science and social science to business. So this course is about a way of thinking that embraces all human endeavors. Two of its highlights, which come towards the end of the semester, are the law of large numbers and the central limit theorem. The latter explains why the normal distribution is, in a sense, “normal”. In addition, this course covers almost all material (except order statistics, percentile, mode, and risk management) in SOA/CAS Exam P. More information on Exam P and actuarial science is in Math 442 (Probability Seminar). Math 442 is a half-credit course, but not a requirement of Math 441.
Recommended Citation
Wu, Zhixin, "MATH 441 Probability Wu Fall 2024" (2024). All Course Syllabi. 946, Scholarly and Creative Work from DePauw University.
https://scholarship.depauw.edu/records_syllabi/946
Student Outcomes
Students completing the course will be able to: (1) Use basic counting techniques (multiplication rules, combinations, and permutations) to compute probability and odds. (2) Compute conditional probabilities directly and using Bayes' theorem, and check for independence of events. (3) Set up and work with discrete random variables. In particular, understand the Bernoulli, Binomial and Poisson distributions. (4) Work with continuous random variables. In particular, know the properties of Uniform, Normal and Exponential distributions. (5) Know what expectation and variance mean and be able to compute them. (6) Compute the covariance and correlation between jointly distributed variables. (7) Understand the law of large numbers and the central limit theorem. (8) Use available resources (the internet or books) to learn about and use other distributions as they arise.