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A dependent variable is a variable whose value depends on the values of one or more other independent variables. This notion comes up regularly in a variety of contexts. In ...

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...

The function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

A financial measure of a fund's sensitivity to market movements which measures the relationship between a fund's excess return over Treasury Bills and the excess return of a ...

Let the absolute frequencies of occurrence of an event in a number of class intervals be denoted f_1, f_2, .... The cumulative frequency corresponding to the upper boundary ...

A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function C_y(tau), spectral ...

The functions E_1(x) = (x^2e^x)/((e^x-1)^2) (1) E_2(x) = x/(e^x-1) (2) E_3(x) = ln(1-e^(-x)) (3) E_4(x) = x/(e^x-1)-ln(1-e^(-x)). (4) E_1(x) has an inflection point at (5) ...

The Hh-function is a function closely related to the normal distribution function. It can be defined using the auxilary functions Z(x) = 1/(sqrt(2pi))e^(-x^2/2) (1) Q(x) = ...

The grouping of data into bins (spaced apart by the so-called class interval) plotting the number of members in each bin versus the bin number. The above histogram shows the ...