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Formally a random variable is considered to be a function on the possible outcomes.

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## Some Related Sentences

Formally and random

__Formally__, dependence refers

**to**any situation in which

__random__variables do not satisfy

**a**mathematical condition of probabilistic independence

**.**

__Formally__,

**a**statistic s

**is**

**a**measurable

**function**of X ; thus,

**a**statistic s

**is**evaluated

**on**

**a**

__random__

**variable**X, taking

**the**value s ( X ), which

**is**itself

**a**

__random__

**variable**

**.**

__Formally__, we begin by considering some family of distributions for

**a**

__random__

**variable**X, that

**is**indexed by some θ

**.**

__Formally__,

**the**algorithm's performance will

**be**

**a**

__random__

**variable**determined by

**the**

__random__bits ; thus either

**the**running time, or

**the**output ( or both ) are

__random__variables

**.**

Formally and variable

__Formally__,

**a**cumulativity predicate CUM can

**be**defined as follows, where capital X

**is**

**a**

__variable__over sets, U

**is**

**the**universe of discourse, p

**is**

**a**mereological part structure

**on**U, and

**is**

**the**mereological sum operation

**.**

__Formally__,

**a**quantization predicate QUA can

**be**defined as follows, where

**is**

**the**universe of discourse, and

**is**

**a**

__variable__over sets, and

**is**

**a**mereological part structure

**on**with < math > < _p </ math >

**the**mereological part-of relation

**.**

__Formally__however they define it as any

__variable__that does not directly affect

**the**fundamentals of

**the**economy

**.**

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students

**to**gain experience in

**a**field of work which

__is__likely

**to**lead

**to**

**a**full-time job

**on**graduation

**.**

__Formally__,

**the**set of all context-free languages

__is__identical

**to**

**the**set of languages accepted by pushdown automata ( PDA ).

More rigorously,

**the**divergence of**a**vector field F at**a**point p__is__defined as**the**limit of**the**net flow of F across**the**smooth boundary of**a**three dimensional region V divided by**the**volume of V as V shrinks**to**p**.**__Formally__,__Formally__,

**the**base

__is__known as Naval Support Facility Diego Garcia (

**the**US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia (

**the**UK's term ).

__Formally__, there

__is__

**a**clear distinction: " DFT " refers

**to**

**a**mathematical transformation or

**function**, regardless of how it

__is__computed, whereas " FFT " refers

**to**

**a**specific family of algorithms for computing DFTs

**.**

__Formally__, oxidation state

__is__

**the**hypothetical charge that an atom would have if all bonds

**to**atoms of different elements were 100 % ionic

**.**

__Formally__, an inner product space

__is__

**a**vector space V over

**the**field together with an inner product, i

**.**e., with

**a**map

__Formally__, if M

__is__

**a**set,

**the**identity

**function**f

**on**M

__is__defined

**to**

**be**that

**function**with domain and codomain M which satisfies

*

__Formally__, when working over**the**reals, as here, this__is__accomplished by considering**the**limit as ε → 0 ; but**the**" infinitesimal " language generalizes directly**to**Lie groups over general rings**.**__Formally__,

**a**profinite group

__is__

**a**Hausdorff, compact, and totally disconnected topological group: that

__is__,

**a**topological group that

__is__also

**a**Stone space

**.**

__Formally__, this sharing of dynamics

__is__referred

**to**as universality, and systems with precisely

**the**same critical exponents are said

**to**belong

**to**

**the**same universality class

**.**

__Formally__,

**a**frame

__is__defined

**to**

**be**

**a**lattice L in which finite meets distribute over arbitrary joins, i

**.**e

**.**every ( even infinite ) subset

Formally and considered

__Formally__, they have always been

__considered__Orthodox Christians, but most of them followed shamanism and animism as

**a**part of their culture

**.**

Formally and be

However, shortly after this positive result, Kurt Gödel published On

__Formally__Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot__be__proved in**the**system**.**__Formally__

**the**" head of state " can also personally

__be__

**the**" head of government " ( ex officio or by ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over

**the**Head of Government and other ministers, whether he

**is**their actual political superior ( absolute monarch, executive president ) or rather theoretical or ceremonial in character

**.**

__Formally__, in

**the**finite-dimensional case, if

**the**linear map

**is**represented as

**a**multiplication by

**a**matrix A and

**the**translation as

**the**addition of

**a**vector, an affine map acting

**on**

**a**vector can

__be__represented as

__Formally__,

**the**convex hull may

__be__defined as

**the**intersection of all convex sets containing X or as

**the**set of all convex combinations of points in X

**.**

__Formally__,

**a**decision problem

**is**P-complete ( complete for

**the**complexity class P ) if it

**is**in P and that every problem in P can

__be__reduced

**to**it by using an appropriate reduction

**.**

__Formally__,

**a**detailed balanced process

**is**

**the**one

**on**which

**the**probability

**to**

__be__in

**the**state x and transit

**to**x ' must

__be__

**the**same as

**to**

__be__in

**the**state x ' and transit

**to**x

**.**

If R

**is****a**ring, let R denote**the**ring of polynomials in**the**indeterminate X over R**.**Hilbert proved that if R**is**" not too large ", in**the**sense that if R**is**Noetherian,**the**same must__be__true for R**.**__Formally__,__Formally__,

**a**unique factorization domain

**is**defined

**to**

__be__an integral domain R in which every non-zero and non-unit x of R can

__be__written as

**a**product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and

**a**unit u:

__Formally__,

**the**problem of supervised pattern recognition can

__be__stated as follows: Given an unknown

**function**(

**the**ground truth ) that maps input instances

**to**output labels, along with training data assumed

**to**represent accurate examples of

**the**mapping, produce

**a**

**function**that approximates as closely as

**possible**

**the**correct mapping

**.**

__Formally__,

**a**government would lay out its reasons for going

**to**war, as well as its intentions in prosecuting it and

**the**steps that might

__be__taken

**to**avert it

**.**

__Formally__,

**the**case where only

**a**subset of parameters

**is**defined

**is**still

**a**composite hypothesis ; nonetheless,

**the**term point hypothesis

**is**often applied in such cases, particularly where

**the**hypothesis test can

__be__structured in such

**a**way that

**the**distribution of

**the**test statistic (

**the**distribution under

**the**null hypothesis ) does not depend

**on**

**the**parameters whose values have not been specified under

**the**point null hypothesis

**.**

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