# 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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Since, at each step, the generation of a discrete random variable is needed, we can use any algorithm that simulates an arbitrary discrete distribution.
Let in general X and Y be discrete random variables taking values x = ([x.
n[Pi]] be the set of discrete random variables taking values [w.
Below are the computational formulas for a discrete random variable with pdf [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and for a continuous random variable with pdf f: R[right arrow]R, respectively:
The inverse transform method can be adjusted for discrete random variables as well, if we consider the generalized inverse of the cdf i.
For describing discrete random variables associated with experiments, an important notion is that of Bernoulli trials.
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.
Walker, An efficient method for generating discrete random variables with general distributions, ACM Trans.
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.

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