This document discusses discrete random variables and their applications in engineering. It defines a random variable as a variable that can take on different possible values from a sample space, like the number of heads in a coin toss. Discrete random variables are defined over a countable sample space and take integer values, while continuous random variables can take any real number value. Examples of applying discrete random variables include determining the probability of circuits being accepted or rejected based on testing, and calculating the number of semiconductor wafers that need analyzing to detect contamination.