# 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.
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:
If X is a discrete random variable, then a better way of describing it is to give its probability distribution function (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])
Probability density function (pdf) A discrete pdf assigns a probability to each possible outcome of the discrete random variable. A continuous pdf is a set function that expresses a distribution in which a probability is assigned to a range of values from a continuous random variable.
Her topics include discrete random variables and expected values, moments and the moment-generating function, jointly continuously distributed random variables, hypothesis tests for a normal population parameter, quantifying uncertainty: standard error and confidence intervals, and information and maximum likelihood estimation.
Roughly speaking, continuous random variables are found in studies with morphometry, whereas discrete random variables are more common in stereological studies (because they are based on the counts of points and intercepts).
general discrete random variables. A distribution and its PGF are denoted by Pr{[S.sub.n] = k} = [s.sub.k] (k [greater than or equal to] 1) and S(z) = [[summation].sup.[infinity].sub.k=1] [s.sub.k][z.sup.k], respectively.
Among the topics are discrete random variables and probability distributions, joint probability distributions and random samples, tests of hypotheses based on a single sample, simple linear regression and correlation, and distribution-free procedures.
The text begins with sets and functions, then covers combinatorics, probability, conditional probability, discrete random variables, and densities.
Theorem 4 (7, Theorem IX.8) Let ([X.sub.n)n [greater than or equal to]1] be a sequence of discrete random variables supported by N, with associated probability generating functions [p.sub.n](u).
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.

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