The Monte Carlo simulation technique, named for the famous Monaco gambling resort, originated during World War II as a way to model potential outcomes from a random chain of events. It is particularly ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

ABSTRACT There is randomness in both the applied loads and the strength of systems. Therefore, to account for the uncertainty, the safety of the system must be quantified using its reliability. Monte ...

This course builds a rigorous foundation of probability. Topics covered include: basic concepts of probability theory and statistics, counting, axioms of probability, independence, Bayes rule, ...