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In mathematics, a variable (from Latin variabilis, "changeable") is a symbol, typically a letter, that refers to an unspecified mathematical object. [1] [2] [3] One says colloquially that the variable represents or denotes the object, and that any valid candidate for the object is the value of the variable. The values a variable can take are ...
A variable of this type is called a dummy variable. If the dependent variable is a dummy variable, then logistic regression or probit regression is commonly employed. In the case of regression analysis, a dummy variable can be used to represent subgroups of the sample in a study (e.g. the value 0 corresponding to a constituent of the control ...
n is a free variable and k is a bound variable; consequently the value of this expression depends on the value of n, but there is nothing called k on which it could depend. In the expression ∫ 0 ∞ x y − 1 e − x d x , {\displaystyle \int _{0}^{\infty }x^{y-1}e^{-x}\,dx,}
The term Variable is relevant to several contexts, and is especially important to mathematics and computer science. Scientists and engineers will often use mathematical variables in formulae and equations, such as E = m c 2; they will also have their own special uses of the term. The term Variable can also occur in other contexts, such as ...
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
The value of a variable or a constant is any number or other mathematical object assigned to it. Physical quantities have numerical values attached to units of measurement. The value of a mathematical expression is the object assigned to this expression when the variables and constants in it are assigned values.
Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].
Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication.