**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)*

*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.