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Informally, a random variable can be described as a variable whose value depends on the outcome of a random or chance phenomenon. Some examples of random variables are: the highway MPG of a new car randomly sampled from all cars on sale, the quality measurement of a product randomly sampled from a production line, the temperature measurement at a particular moment and location of a machine where temperature randomly varies over time. Due to the ubiquitous uncertainty and variation existing in industrial systems and processes, most variables of interest in industrial data analytics applications can be considered as random variables. Many industrial data analytics problems involve multiple random variables, which form a vector of random variables, also called as a random vector. In this chapter, we study the concept of random vectors and the multivariate normal distribution, the most commonly used model for a random vector.