The theory of signals and systems is applied for processing of signals like speech, radio detection and ranging, sound navigation and ranging, earthquake, electrocardiogram, and electroencephalogram. All these are naturally occurring signals and hence have some random components. This chapter introduces the principles of random signals for an in-depth understanding of the processing methods. It presents the concept of probability, conditional probability, and Bayes’ theorem. The chapter introduces the concept of set theory. It discusses the probability distribution function and density functions for discrete and continuous random variables. A set is said to be countable if it has countable number of elements in it corresponding to integers 1, 2, 3, and so on, and it is said to be uncountable if it has elements that are not countable. If a set contains no element, it is said to be an empty set or a null set. Geometrical or diagrammatic representation to work with sets is called the Venn diagram.