In other words, if all choices of the random variable are equally likely, the number of values (or the length, if it is a continuous random variable) needed for the random variable to keep the same amount of information as the given distribution is a measure of diversity.

For each arc, say, (i, j), there is a loss factor, [[alpha].sub.ij], which is a continuous random variable in interval [0, 1] and shows the fraction of nominal capacity that is wasted.

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.

In reality, corn prices can and do take on any value such as $1.71 3/4 or $2.31 1/4, or are more correctly stated as being a continuous random variable. 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.

A continuous pdf is a set function that represents a distribution in which a probability is assigned to a range of values from a continuous random variable. The continuous pdf assigns a probability to the range 3.15 to 3.25 for the continuous random variable X, the diameters of shafts produced by a farm machinery company (figure 4.1).

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.