Introduction to Monte Carlo (MC) Method: Random Variables in Stochastic Models

Abstract

According to its definition, stochastic simulation model should contain at least one random variable (Snopkowski 2007). Random variable, being a numerical representation of the outcome of a random experiment, is a key term in statistical analysis (Barańska 2008) and, as observed by Snopkowski (2007), is an essential element of every stochastic simulation. In literature, there are a number of different definitions of a random variable. Stanisz (2006) defines random variable as a “function determined on an elementary event space, which assigns a real number with defined probability to every elementary event. Therefore, this value cannot be predicted in advance, as it depends on a random event.” A similar definition is provided by Barańska (2008). As claimed by Benjamin and Cornell (1977), random variable is “a variable that assumes numerical values whose outcome cannot be predicted with complete certainty.” Bobrowski (1980), on the other hand, defines random variable as “a variable that, as a result of an experiment, can assume, with defined probability, one of the values of a certain set of real numbers”, and Aczel (2000) states that “random variable is a variable whose assumed values depend on chance”. Sokołowski (2004), however, apart from quoting a popular definition of random variable, analyses the instances of carelessness and errors that he has encountered in many other studies, regarding random variables.