One-Dimensional Random Variables
Frank E. Beichelt · 2018
Basically, application of a real function to the outcomes of a random experiment does not change the &s;nature&s; of the random experiment. When discussing random variables, the original, application-oriented random experiment will play no explicit role anymore. Thus, a random variable can be considered to be an abstract formulation of a random experiment. The probability distribution of a discrete random variable Y is given by assigning to each possible value of Y its probability according to the probability mass function of Y. This approach is no longer feasible for random variables, which can assume non-countably many values. If a random variable X has a density f (x), then its distribution function need not exist in an explicit form. The probability distribution function and/or the density of a continuous random variable X contain all the information on X.