Random Variables and Their Distributions

Abstract

The purpose of performing experiments and collecting data is to gain information on certain quantities of interest called random variables. The exact value of these quantities cannot be known with absolute precision, but rather we can constrain the variable to a given range of values, narrower or wider according to the nature of the variable itself and the type of experiment performed. Random variables are described by a distribution function, which is the theoretical expectation for the outcome of experiments aimed to measure it. Other measures of the random variable are the mean, variance, and higher-order moments.