CHAPTER 2 - RANDOM VARIABLES

Abstract

This chapter describes random variables. A random variable is a variable that assumes, as a result of a trial, only one of the set of possible values and with which is connected some field of events representing its occurrences in given sets, contained in the main field of events δ. Random variables may be both scalar and vector. In correspondence with general definition of a vector, one can call a vector random variable or a random vector any ordered set of scalar random variables. A random variable with countable or finite set of possible values is called a discrete random variable. The distribution of a discrete random variable is completely determined by the probabilities of all of its possible values. It is impossible to determine the distribution of a random variable with an uncountable set of possible values by the probabilities of its values. Therefore, another approach to such random variables is necessary.