Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, "Probability is the most important concept in modern science, especially as nobody has the ...

Objective probability estimates the odds of an event occurring through data analysis. It uses concrete measures instead of guesses to provide a reliable forecast.

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, Chernoff bounds and large deviations, martingales, ...

Investopedia contributors come from a range of backgrounds, and over 25 years there have been thousands of expert writers and editors who have contributed. Thomas J Catalano is a CFP and Registered ...