Independent Identically Distributed (IID) Random Variables

Independent Identically Distributed (IID) random variables are a set of random events or data points that share two key properties: they come from the same probability distribution, meaning they have the same chances of occurring, and each one occurs independently, so the outcome of one does not influence or change the likelihood of others. For example, flipping a fair coin multiple times results in IID variables—each flip has a 50% chance of heads or tails, and one flip's result does not affect the others. IID variables are fundamental in probability and statistics for modeling and analysis.