Then, at the next step, [X.sub.1] is a discrete random variable
taking the values j,j = 1,...,n with probabilities [p.sub.ij] from row i of the matrix P.
The above definition applies to discrete random variables
; for random variables with continuous probability distributions differential entropy is used, usually along with the limiting density of discrete points.
Define the vector b(l, [Delta]) corresponding to the discrete random variable
B(L, [Delta]) taking values [b.sub.i]([l.sub.i], [Delta]) with probabilities [[Pi].sub.i]:
For instance, in the coin-tossing game we can build a discrete random variable
X that takes the value 1 if the event "head" is realized and the value minus 1 if the event "tail" is realized.
If X is a discrete random variable
, then a better way of describing it is to give its probability distribution function (also pdf), an array that contains all its values [x.sub.i], and the corresponding probabilities with which each value is taken [p.sub.i] = P(X = [x.sub.i]),
Klerides and Hadjiconstantinou  researched time-cost tradeoff problem of activity period when it was a discrete random variable
and proposed a two-stage stochastic integer programming approach based on path.
It uses the vast quantity of available baseball records to teach such matters as descriptive statistics for one quantitative variable, sports betting, probability distribution functions for a discrete random variable
, confidence intervals, and streaking.
Suppose that N is a discrete random variable
with the property that P(N = n) > 0 for each positive integer n.
The method used to construct a time series of a probability that a discrete random variable
X = x, x = 1, 2 is conditioning on another discrete random variable
Y, Y = 1, 2, 3 which is observable both in the archaeological record and in an ethnographic cross-cultural database.
Assume we draw a random sample of n animals from the pen and we have the discrete random variable
X that takes on the value 1 for a success (getting a female, F) and a value of 0 for a failure.
If the set of values that X takes is at most countable, then X is a discrete random variable
, if it is an interval in [??], then X is a continuous random variable
Therefore, the weather can be modelled as a discrete random variable
. In this situation, activity durations considering both fuzzy factors and random factors can be modelled as fuzzy random variables as shown in Figure 2.