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A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. [ 1 ] [ 2 ] Set-valued functions are used in a variety of mathematical fields, including optimization , control theory and game theory .
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
We assume that the probabilities of these outcomes are given by p 1 (x), p 2 (x), p 3 (x), p 4 (x), p 5 (x), all of which are functions of some independent variable(s) x. Then, for a fixed value of x, the logarithms of the odds (not the logarithms of the probabilities) of answering in certain ways are:
For example: If stock=0 Then message= order new stock Else message= there is stock End If. In the example code above, the part represented by (Boolean condition) constitutes a conditional expression, having intrinsic value (e.g., it may be substituted by either of the values True or False) but having no intrinsic meaning
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
This parser function can be used to detect whether a template parameter is defined, even if it has been set to a false value. For example, to check whether the first positional parameter has been passed to a template (note that the strings "+" and "-" can be any two different non-whitespace strings):
An appropriate value of p in the ARMA(p, q) model can be found by plotting the partial autocorrelation functions. Similarly, q can be estimated by using the autocorrelation functions. Both p and q can be determined simultaneously using extended autocorrelation functions (EACF). [9]
where is a vector of observations , and denotes the matrix of stacked values observed in the data. If the sample errors have equal variance σ 2 {\displaystyle \sigma ^{2}} and are uncorrelated , then the least-squares estimate of β {\displaystyle {\boldsymbol {\beta }}} is BLUE (best linear unbiased estimator), and its variance is estimated with