Introduction

We start our investigation of random variables. Descriptive statistics deals with variables that can take values within a discrete or a continuous set. Correspondingly, we cover discrete random variables. As we shall see, the mathematics involved in the study of continuous random variables requires concepts from calculus and is a bit more challenging than what is needed to cope with discrete ones. Hence, we prefer to proceed gradually, introducing intuitive concepts in the simpler case and emphasizing an intuitive link with descriptive statistics.

In Section 6.1 we introduce random variables formally, as associations of random events with numerical values. Then, in Section 6.2 we show how the distribution of a discrete random variable can be characterized by a probability mass function or a cumulative distribution function, which are related to concepts from descriptive statistics, i.e., histograms of relative frequencies and cumulative relative frequencies. Sections 6.3 and 6.4 proceed along the same conceptual path, introducing expected values of discrete random variables first, and then variance and standard deviations. Finally, in Section 6.5 we describe the main discrete probability distributions that are common in applications, along with some motivating examples relevant to business management.

As we pointed out, this is just a first step providing the reader with the basic knowledge about probability distributions, which is needed to tackle continuous random variables where we also cover other concepts such as quantiles, skewness, and kurtosis; these apply to both discrete and continuous random variables, but we prefer treating them once within a more complete setting, after building some intuition based on the simpler, discrete case. The next one we just consider the univariate case; We introduce concepts about independence and correlation among multiple random variables, thus stepping into the domain of multivariate distributions.