Discrete Spaces of Elementary Events

Abstract

Section 1.1 introduces the fundamental concept of probability space, along with some basic terminology and properties of probability when it is easy to do, i.e. in the simple case of random experiments with finitely or at most countably many outcomes. The classical scheme of finitely many equally likely outcomes is discussed in more detail in Sect. 1.2. Then the Bernoulli scheme is introduced and the properties of the binomial distribution are studied in Sect. 1.3. Sampling without replacement from a large population is considered, and convergence of the emerging hypergeometric distributions to the binomial one is formally proved. The inclusion-exclusion formula for the probabilities of unions of events is derived and illustrated by some applications in Sect. 1.4.