R is at most countable in R, then X is a discrete random variable, otherwise, it is a

continuous random variable.

18] studied generalization of Tukey's g-h family of distributions, when the standard normal random variable is replaced by a

continuous random variable U with mean 0 and variance 1.

For a source that is characterized as a

continuous random variable with PDF p(x) the N-point nonuniform scalar quantizer distortion could be defined as the expected mean square error between original and quantized signal.

Let X be a

continuous random variable with probability density function f (x), the basic measure of uncertainty is given by Shannon [18] and is defined as

We say that X is

continuous random variable if its place of results is some interval and if its distribution function F(x) in this interval can continuously be derived.

To this aim we introduce definitions of discrete, continuous and absolutely continuous random closed set, coherently with the classical 0-dimensional case, in order to propose an extension of the standard definition of discrete, continuous, and absolutely

continuous random variable, respectively.

A

continuous random variable coupled with a large number of observations over a sufficiently long enough time produces a distribution of random variables with unique characteristics.

For a

continuous random variable f(x) interpreted as dF(x)/dx is the probability density function (pdf).

25 for the

continuous random variable X, the diameters of shafts produced by a farm machinery company (figure 4.

A

continuous random variable is defined by the values it takes (often a mathematical function) and also by the probabilities of getting those values, which are related to the probabilities of the events in math.

then X is a

continuous random variable and f is called its probability density function (pdf).

That function f is called the probability density function (pdf) of the

continuous random variable X.