STAT 451 - Probability Theory for Data Science and Statistics (3)

After a short and rapid refresher on the axioms of probability, univariate random variables and their transformations, CDF, PDF, PMF, MGF and their properties, the course will cover several probability inequalities including Markov, Chebyshev, Jensen; the Weak Law of Large Numbers; the Central Limit Theorem with a proof based on the MGF; introduction to Borel sigma-algebra and null sets; almost sure convergence; Borel-Cantelli Theorem and the Strong Law of Large Numbers; convergence in distribution in details; Slutsky’s Theorem; multivariate random variables in depth, including multivariate transformations and the use of the Jacobean; details on the multivariate Normal distribution and its properties including discussions on conditional distributions, transformations and quadratic forms.

Grading: Graded/Satisfactory Unsatisfactory/Audit
Course ID: 57064
Consent: No Special Consent Required
Components: Lecture
Course Equivalents: STAT 451H
Prerequisite: MATH 251 and STAT 355 with a grade of ‘C’ or better.