Exponential distribution

The exponential distribution describes the waiting time between events in a process where events occur randomly and independently at a constant average rate. For example, it can model the time between customer arrivals at a store or the time until a machine breaks down. The key idea is that, on average, events happen at the same rate, but the actual waiting times can vary; sometimes they are short, other times longer. It’s characterized by a parameter that represents the average rate of occurrence—faster rates mean shorter waiting times. This distribution is useful in reliability, queuing theory, and survival analysis.