ABSTRACT
A basic knowledge of probability theory and stochastic processes is necessary for proper and judicious application of wavelet transform theory. This chapter provides an overview of probabilistic tools and techniques to study nondeterministic events. It presents descriptions of average measures such as expectation of a random variable. Typical second-order measures, and the concept of independent random variables. Probability theory is developed on the basis of a set of postulates. These postulates were first promulgated by A. N. Kolmogorov in the year 1933. In these postulates, an experiment is a mental or physical activity which produces a measurable outcome. A random variable, distribution function, probability mass function, and probability density function are defined. A real-valued random variable is either discrete or continuous. Some useful second-order expectations of a single random variable are variance, standard deviation, and squared coefficient of variation. A sequence of random variables which are indexed by some parameter, say time, are called stochastic processes.
