MATH 3332

Introduction to Mathematical Probability

0.5 credits · Undergraduate

Fall 2025

Topics

As a mathematical introduction to the theory and applications of probability, topics include sample spaces
and events, permutations and combinations, binomial coefficients, the probability of an event, some rules
of probability, conditional probability, independent events, Bayes’ Theorem, probability distributions
discrete random variables, continuous random variables, probability density functions, joint distributions
marginal distributions, conditional distributions, the expected value of a random variable, moments
Chebyshev’s Theorem, moment-generating functions, conditional expectations, some special probability
distributions such as the discrete uniform distribution, the Bernoulli distribution, the binomial
binomial distribution, the bivariate normal distribution, etc., functions of random variables, and limit
Successful students of this course
Calculate probabilities and conditional probabilities by working with sets that represent the events
and by using some fundamental counting principles and the rules of probability
Understand the concept of independent events and apply our understanding of independent events
to real-life scenarios
Use the law of total probability and Bayes’ theorem to calculate probabilities of some complex
events

Book 1 Introduction to Probability and Statistics, 4th Edition, by J. S. Milton and Jesse C. Arnold Paper copies of this

Fall 2019

As a mathematical introduction to the theory and applications of probability, topics include sample spaces
and events, permutations and combinations, binomial coefficients, the probability of an event, some rules
of probability, conditional probability, independent events, Bayes’ Theorem, probability distributions
discrete random variables, continuous random variables, probability density functions, joint distributions
marginal distributions, conditional distributions, the expected value of a random variable, moments
Chebyshev’s Theorem, moment-generating functions, conditional expectations, some special probability
distributions such as the discrete uniform distribution, the Bernoulli distribution, the binomial
binomial distribution, the bivariate normal distribution, etc., functions of random variables, and limit
Successful students of this course
Calculate probabilities and conditional probabilities by working with sets that represent the events
and by using some fundamental counting principles and the rules of probability
Understand the concept of independent events and to apply our understanding of independent
events to real-life scenarios
Use the law of total probability and Bayes’ theorem to calculate probabilities of some complex
events

Book 1 Introduction to Probability and Statistics, 4th Edition, by J. S. Milton and Jesse C. Arnold

Sources