# HW 3160 Fall 2018

Catalog description: Introduction to the theory of probability. Sets and counting, probability axioms, conditional probabilities, random variables, limit theorems. Three credits. Prerequisite: MATH 2110Q2130Q or 2143Q.

Open source educational materials are provided (no textbook is necessary for this course)

Current sections of Math 3160

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.