ABSTRACT
This chapter discusses probability, multiplicity, combinatorics, averages, and distribution functions and provides a foundation for describing entropy. Probabilities are quantities in the range from zero to one. If only one outcome is possible, the process is deterministic—the outcome has a probability of one. An outcome that never occurs has a probability of zero. Some problems in probability cannot be solved directly by applying the addition or multiplication rules. Such questions can usually be reformulated in terms of composite events to which the rules of probability can be applied. Bayes' rule, a combination of equations can help us compute hard-to-get probabilities from ones that are easier to get. A probability distribution function contains all the information that can be known about a probabilistic system. A full distribution function, however, is rarely accessible from experiments. Generally, experiments can measure only certain moments of the distribution. The square root of the variance is s, which is also called the standard deviation..
