# Z94.1 - Analytical Techniques & Operations Research Terminology

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VALUE OF A GAME. The number v (expected payoff) associated with any two-person zero-sum game for which the minimax theorem (q.v.) holds. 

VARIABLE. Generally, any quantity which varies. More precisely, a variable in the mathematical sense, i.e., a quantity which may take any one of a specified set of values. It is convenient to apply the same word to denote nonmeasurable characteristics, e.g., “sex” is a variable in this sense since any human individual may take one of two “values,” male or female. It is useful, but far from being the general practice, to distinguish between a variable as so defined and a random variable or variate (q.v.). [22:310, 7:422]

VARIANCE. A measure of the squared dispersion of observed values or measurements expressed as a function of the sum of the squared deviations from the population mean or sample average.

VARIATE. In contradistinction to a variable (q.v.) a variate is a quantity which may take any of the values of a specified set with a specified relative frequency or probability. The variate is therefore often known as a random variable. It is to be regarded as defined, not merely by a set of permissible values like an ordinary mathematical variable, but by an associated frequency (probability) function expressing how often those values appear in the situation under discussion. [22:312, 4:26, 13:1993]

VECTOR. An ordered set or array of quantities, usually n real numbers (x1, x2,...x). A vector arrayed horizontally is called a row vector; one arrayed vertically is called a column vector. For example, the rows of a matrix are row vectors, the columns of a matrix are column vectors. 

VENN DIAGRAM. A schematic representation of the universal set and its subsets. A rectangle is usually used to represent the universal set, points to designate elements of the set and circles to depict subsets of the universal set. The diagram is sometimes referred to as an Euler Diagram.

VERTEX. A point of a convex set which does not lie on a line segment joining any other two points of the set; also called an extreme point. Sometimes used as a synonym for node (q.v.). 

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