A function that does not change sign when the sign of the independent variable is changed, i.e. satisfying the condition $f(-x)=f(x)$. The graph of an eve
A function that does change sign when the sign of the independent variable is changed, i.e. satisfying the condition $f(x)=-f(-x)$, is called an [[Odd
404 bytes (71 words) - 14:14, 10 April 2014
...s also defined for discrete distributions: If the values $x_k$ of a random variable $X$ with distribution $p_k = \mathsf{P}(X = x_k)$ are arranged in increasin
...istics)]] the mode acts as a measure of location of the values of a random variable. For distributions which are unimodal and symmetric with respect to some po
2 KB (243 words) - 20:49, 14 December 2015
Here $z$ is a complex variable, $m$ is an integer and $n$ is a natural number. The series converge in the
...<TD valign="top"> A.I. Markushevich, "Theory of functions of a complex variable" , '''3''' , Chelsea (1977) pp. Chapt. 8 (Translated from Russian)</TD><
1 KB (199 words) - 17:44, 1 November 2014
...f. [[Convex function (of a complex
variable)|Convex function (of a complex
variable)]]), <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.
...valign="top"> G.M. Goluzin, "Geometric theory of functions of a complex
variable" , ''Transl. Math. Monogr.'' , '''26''' , Amer. Math. Soc. (1969) (Transl
4 KB (623 words) - 17:10, 7 February 2011
...em is one of the classical results in the theory of functions of a complex variable of the type of [[Distortion theorems|distortion theorems]].
...TD> <TD valign="top"> S. Stoilov, "The theory of functions of a complex variable" , '''1–2''' , Moscow (1962) (In Russian; translated from Rumanian)</TD
3 KB (454 words) - 08:12, 6 June 2020
The inverse hyperbolic functions of a real variable $ x $
The inverse hyperbolic functions of a complex variable $ z $
3 KB (487 words) - 19:15, 17 January 2024
...i=1,\dotsc,m$; $j=1,\dotsc,m_i$) is either a variable or the negation of a variable, and $\bot$ is the logical symbol denoting falsehood. For each propositiona
803 bytes (132 words) - 13:03, 14 February 2020
...n of values of the [[Normal distribution|normal distribution]] of a random variable at a distance from its [[Mathematical expectation|mathematical expectation]
Let $X$ be a normally $N(a,\sigma^2)$ distributed random variable. For any $k>0$,
1 KB (223 words) - 00:44, 24 December 2018
...ing time (relative to this family of subalgebras) is a mapping (a [[random variable]]) $\tau : \Omega \rightarrow T \cup \{\infty\}$ such that
...iable. This condition has the interpretation that the (time-valued) random variable $\tau$ has no knowledge of the future, since the $\sigma$-algebra $\mathcal
2 KB (318 words) - 19:06, 11 October 2017
The probability distribution of the random variable
is a random variable subject to the standard normal law $ N( 0, 1) $
5 KB (724 words) - 14:55, 7 June 2020
is a real or complex variable. If $ a _ {0} \neq 0 $,
...lane, that is, it is an [[Entire function|entire function]] of the complex variable $ z $,
2 KB (328 words) - 19:37, 5 June 2020
...mula is a formula; and b) if $A$ and $B$ are formulas and $y$ is an object variable, then $(\neg A)$, $(A\mathbin\&B)$, $(A\lor B)$, $(A\supset B)$, $(\forall
2 KB (252 words) - 16:42, 30 December 2018
...f Cauchy distributions is closed under linear transformations: If a random variable $ X $
then the random variable $ Y = aX + b $
4 KB (498 words) - 15:35, 4 June 2020
cf. [[Random variable|Random variable]]). For $ m < N $,
4 KB (507 words) - 22:10, 5 June 2020
...makes it possible to reduce the study of the deformation of surfaces with variable $ K > 0 $
...r-reaching analogy between the properties of deformations of surfaces with variable and constant positive Gaussian curvature.
1 KB (168 words) - 08:28, 6 June 2020
be a random variable having a continuous and strictly increasing distribution function $ F $.
Then the random variable $ Y = F ( X) $
4 KB (562 words) - 20:33, 16 January 2024
The distribution of a discrete random variable assuming non-negative integral values $ m = 0, 1 \dots $
The random variable equal to the number of independent trials prior to the first successful out
1 KB (202 words) - 19:41, 5 June 2020
''conditional expectation, of a random variable''
...ctation of $X$ with respect to $\mathfrak{B}$ is understood to be a random variable $\mathsf{E}(X\, |\, \mathfrak{B})$, measurable with respect to $\mathfrak{B
4 KB (642 words) - 11:43, 14 June 2017
...depending on a continuous or discrete argument $\tau$, relative to another variable $\phi(\tau)$ whose behaviour, as a rule, is assumed to be known. In general
...lign="top"> A.F. Timan, "Theory of approximation of functions of a real variable" , Pergamon (1963) (Translated from Russian)</TD></TR><TR><TD valign="top
2 KB (326 words) - 09:43, 26 April 2014
A property of the dependence of one random variable on another, defined by the fact that the conditional variance is equal to a
280 bytes (45 words) - 17:14, 7 February 2011