Probability and Random Variables

This introductory chapter of the book presents the gist of probability theory. It first discusses the probability space, and the conditional probability and independence. The chapter then introduces the concept of the random variable with an example. A random variable that takes integer values is called a discrete random variable. A random variable that takes values in R is called a continuous random variable. The chapter explains expectation and variance of a random variable. It also discusses joint cumulative probability distribution function and moment generating functions. Further, the chapter describes some well-known probability inequalities that enable us to derive bounds on probabilities of random variables when only their mean and variance are known. Finally, it explains multivariate normal distribution. Controlled Vocabulary Terms conditional probability; continuous random variable; discrete random variable; joint probability distribution; moment-generating function; multivariate normal distribution; probability inequalities; probability space; probability theory; random variables