4 - Models for the Ramdom Error

Abstract

Models for the random error are called random variables. A random variable is a function that maps experimental outcomes to real numbers. For example, Y - the number of heads obtained in tossing a coin once, is a random variable that maps the experimental outcomes of a head or a tail to the numbers 1 and 0, respectively. If the experimental outcome is already a real number, then the outcome itself is a random variable. Every random variable has associated with it a distribution function that assigns probabilities to the possible values of the random variable. Distribution functions are specified by either a probability density function or a probability mass function, which emulate a histogram (that has been scaled so its area is equal to one) for a random sample of y values. If the response variable Y is continuous, then its probabilities are specified by a probability density function f (y), which is continuous. If the response variable Y is discrete, then its probabilities are specified by a probability mass function P(Y = k), which is discrete.