Random Variables, Densities, and Cumulative Distribution Functions

Abstract

It is natural for the outcomes of many experiments in the real world to be measured in terms of real numbers. For example, measuring the height and weight of individuals, observing the market price and quantity demanded of a commodity, measuring the yield of a new variety of wheat, or measuring the miles per gallon achievable by a new hybrid automobile all result in real-valued outcomes. The sample spaces associated with these types of experiments are subsets of the real line or, if multiple values are needed to characterize the outcome of the experiment, subsets of n-dimensional real space, $$ {\mathbb{R}^n} $$ .