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.sub.1],..., [x.sub.n]) and y = ([y.sub.1],..., [y.sub.n]) with a common set of probabilities [Mathematical Expression Omitted], pertaining to a set of relevant states of nature 1,..., n.
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.
