ABSTRACT
A random variable may be defined as a real-valued function defined over the sample space S of a random experiment. The domain of the function is S, and the real numbers associated with the various possible outcomes of the random experiment constitute the range of the function. If the range of the random variable consists of a finite number or countable infinitude of values, the random variable is classified as discrete. If the range consists of a noncountable infinitude of values, the random variable is classified as continuous. A set has a countable infinitude of values if they can be put into one-to-one correspondence with the positive integers. The positive even integers, for example, consist of a countable infinitude of numbers. The even integer 2n corresponds to the positive integer n for n = 1 , 2 , 3 , … https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429124754/be33da89-95f5-45e7-a067-f2fa13b8eb97/content/eq225.tif"/> The real numbers in the interval (0,1) constitute a noncountable infinitude of values.
