Fundamentals of Probability

4 credits · Graduate School

This course is the first in a two-course series on probability and statistical inference that introduces and explores the probabilistic framework underling statistical theory. Students learn probability theory—the formal language of uncertainty—and its application to everyday statistical concepts and analysis methods. Topics include probability axioms, probability and sample space, events and random variables, transformation of random variables, probability inequalities, independence, discrete and continuous distributions, expectations and variances, conditional expectation, moment generating functions, random vectors, convergence concepts (in probability, in distribution, and almost surely), weak and strong law of large numbers, central limit theorem, delta method, order statistics, and exponential family. This course is open to biostatistics students only; for students in other programs, instructor permission is required to enroll. [4]