# Discrete random variable

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## Discrete random variable

A random variable that can take only a certain specified set of individual possible values-for example, the positive integers 1, 2, 3, . . . For example, stock prices are discrete random variables, because they can only take on certain values, such as \$10.00, \$10.01 and \$10.02 and not \$10.005, since stocks have a minimum tick size of \$0.01. By way of contrast, stock returns are continuous not discrete random variables, since a stock's return could be any number.

## Discrete Random Variable

A variable that can take only one of several definite values. For example, one's FICO score is a discrete random variable because it can only be a positive integer between 300 and 850.
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Consider a discrete random variable X with values in the set X = {[x.sub.i], i [member of] [N.sub.n]}.
Given any discrete random variable X with n possible outcomes, the Shannon entropy H(X) of the variable X is defined as the function of the probability p of all outcomes of X:
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]),
In particular, we approximate the sequence of conditional normal random variables by a sequence of discrete random variables. Given this period's logarithmic price and conditional variance, the conditional normal distribution of the next period's logarithmic price is approximated by a discrete random variable that takes on 2n + 1 values for each asset.
Let [S.sub.n[Pi]] be the set of discrete random variables taking values [w.sub.1] [less than or equal to] ...
He covers the basics of probability, counting problems, conditional probability and independence, expected value and variance, discrete random variables, and a wide variety of other related subjects over the course of the bookAEs eight chapters and three appendices.
For describing discrete random variables associated with experiments, an important notion is that of Bernoulli trials.
Apparently, the MAC layer latency and jitter are discrete random variables, since the time unit used in transmission is a timeslot.
Among the topics are data description and treatment, probability distributions for discrete random variables, multiple random variables, fundamental statistical analysis, confidence intervals and sample size determination, and reliability analysis of components.
of Texas at Dallas) provides MATLAB computer codes along with detailed examples and exercises with direct connections to the front lines, moving efficiently from basic probability to discrete random variables and their distributions, continuous distributions, computer simulations and Monte Carlo methods, stochastic processes, queuing systems, basic statistics, statistical inference, and regression.
The delayed times, denoted by {[W.sub.i], i [greater than or equal to] 1}, are i.i.d discrete random variables having an arbitrary distribution [w.sub.j] = P{[W.sub.i] = j}, j [greater than or equal to] 1 with PGF w(z) = [[summation].sup.[infinity].sub.j = 1] [w.sub.j][z.sup.j], [absolute value of z] < 1.
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.

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