Conditional Probability and Independence

Abstract

Both conditional probability and independence are fundamental concepts for probabilists and statisticians alike. Conditional probabilities correspond to updating one’s beliefs when new information becomes available, a natural human instinct. Independence corresponds to irrelevance of a piece of new information, even when it is made available. Additionally, the assumption of independence can and does significantly simplify development, mathematical analysis, and justification of tools and procedures. Indeed, nearly every key result in probability and statistics was first derived under suitable independence assumptions and then extended to selected cases where independence may be lacking. These two topics together also provide the reader with a supply of fascinating problems and often very pretty solutions.