ABSTRACT
This chapter introduces concepts from probability and combinatorics needed for statistical mechanics. Probabilities defined on continuous sample spaces are referred to as probability densities. Probabilities defined on discrete sample spaces are referred to as discrete probabilities. Calculating probabilities is an exercise in counting (the number of elementary events in various sets). The collection of probabilities associated with the range of values of a random variable is known as a probability distribution. A broad class of experiments involve continuous sample spaces on which continuous random variables are defined. Moments characterize the shape of probability distributions. Probability thrives on the repeatability of experiments. A probability distribution is determined by its moments, all of them (when they exist); knowledge of just the mean and the variance are in general insufficient. Calculating probabilities relies on the ability to count the number of elementary events in various sets.
