Exponential random variables: theory and applications

This lecture covers the study of stochastic processes indexed by continuous time, focusing on exponential random variables. The instructor explains the properties of exponential distributions, such as memorylessness and the existence of a constant. The lecture delves into the theory behind exponential random variables and their applications in various scenarios, including Markov chains. Key concepts include the memoryless property, the distribution of exponential random variables, and the independence of random variables. The lecture concludes with a discussion on explosions and theorems related to independent exponential random variables.