The moment-generating function is an alternative specification of a real-valued random variable's probability distribution. It can be used to compute the moments of a distribution and can be extended to vector- or matrix-valued random variables. Not all random variables have moment-generating functions, unlike the characteristic function.

This course dives into the use of randomness in algorithms and data structures, emphasizing the theoretical foundations of probabilistic analysis. Topics range from tail bounds, Markov chains, to randomized algorithms. The concepts are applied to machine learning, networking, and systems. Prerequisites indicate intermediate-level understanding required.