Catalog description: Introduction to the theory of probability. Sets and counting, probability axioms, conditional probabilities, random variables, limit theorems. Three credits. Prerequisite: MATH 2110Q, 2130Q or 2143Q.
Open source educational materials are provided (no textbook is necessary for this course)
Sections of Math 3160 can be found here (Fall 2021) (or here or Spring 2019 or Fall 2019 or Spring 2020 or Fall 2020 or Spring 2021).
Standard syllabus for Math 3160 Probability:
- Combinatorics: product rule and permutations; combinations.
- Axioms of Probability: sample spaces, events and set operations; probability axioms.
- Conditional Probability and Independence: conditional probability and Bayes’ rule; probability trees; independent events.
- Discrete Random Variables: probability mass function (PMF), cumulative distribution function (CDF); expectation; variance, moments, moment generating function (MGF). Uniform, Bernoulli, Binomial, Poisson, Geometric, Hypergeometric distributions; expectation, variance, MGF of these RVs.
- Continuous Univariate Random Variables: probability density function (PDF), CDF, expectation, variance, moments, MGF. Uniform, Exponential, Gamma, Normal distributions; expectation, variance, MGF of these RVs. Transformations (functions) of continuous RVs.
- Jointly Distributed Random Variables: joint PMF/PDF, and CDF; marginal distributions; conditional PMF/PDF; conditional expectation and variance; covariance and correlation coefficients.
- Limit Theorems: Weak Law of Large Numbers, Central Limit Theorem, Normal approximations.