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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.

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## Some Related Sentences

Formally and statistic

__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

**.**

__Formally__

**,**if T

**is**

**a**complete sufficient

__statistic__for θ and E

**(**g

**(**T )) = τ

**(**θ ) then g

**(**T )

**is**

**the**minimum-variance unbiased estimator

**(**MVUE )

**of**τ

**(**θ ).

Formally and s

__Formally__

**,**

**the**problem can be stated as follows: given

**a**desired property

**,**expressed as

**a**temporal logic formula p

**,**and

**a**structure M with initial state

__s__

**,**decide if

**.**

__Formally__

**the**euro

**is**

**the**only legal tender in Büsingen

**;**however

**,**

**the**Swiss franc

**is**far more popular in everyday use as shopping

**is**generally done in nearby Schaffhausen instead

**of**across

**the**border

**(**

__s__) in Germany

**.**

__Formally__

**,**

**a**mortgage lender

**(**mortgagee

**),**or other lien holder

**,**obtains

**a**termination

**of**

**a**mortgage borrower

**(**mortgagor )'

__s__equitable right

**of**redemption

**,**either by court order or by operation

**of**law

**(**after following

**a**specific statutory procedure ).

__Formally__

**,**

**a**composite number n = d · 2 < sup >

__s__</ sup > + 1 with d being odd

**is**called

**a**strong pseudoprime to

**a**relatively prime base

**a**when one

**of**

**the**following conditions hold:

__Formally__

**,**however

**,**there

**is**an examination board consisting

**of**

**a**candidate ’

__s__teachers / examiners

**,**

**the**headmaster / headmistress and

**a**Vorsitzende

**(**r )

**(**head

**),**usually

**a**high-ranking school official or

**the**head

**of**another school

**.**

__Formally__established in 1922

**,**over

**the**decades Woodcraft Rangers has modified Seton ’

__s__original emphasis

**on**outdoor life to incorporate activities that meet

**the**needs

**of**an increasingly urban population

**,**but

**the**goal

**of**changing behavior and encouraging positive outcomes through interaction and education remains central to its mission today

**.**

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 measurable

__Formally__

**,**

**a**

__measurable__cardinal

**is**an uncountable cardinal number κ such that there exists

**a**κ-additive

**,**non-trivial

**,**0-1-valued measure

**on**

**the**power set

**of**κ

**.**

Formally and function

__Formally__

**,**

**the**discrete cosine transform

**is**

**a**linear

**,**invertible

__function__

**(**where denotes

**the**set

**of**real numbers

**),**or equivalently an invertible N × N square matrix

**.**

__Formally__

**,**we are given

**a**set

**of**hypotheses and

**a**set

**of**manifestations

**;**they are related by

**the**domain knowledge

**,**represented by

**a**

__function__that takes as an argument

**a**set

**of**hypotheses and gives as

**a**result

**the**corresponding set

**of**manifestations

**.**

__Formally__

**,**

**a**

__function__ƒ

**is**real analytic

**on**an open set D in

**the**real line if for any x < sub > 0 </ sub > in D one can write

__Formally__

**,**an elliptic

__function__

**is**

**a**

__function__meromorphic

**on**for

**which**there exist two non-zero complex numbers and with

**(**in other words

**,**not parallel

**),**such that and for all

**.**

__Formally__

**,**if

**is**an open subset

**of**

**the**complex plane

**,**

**a**point

**of**

**,**and

**is**

**a**holomorphic

__function__

**,**then

**is**called

**a**removable singularity for if there exists

**a**holomorphic

__function__

**which**coincides with

**on**

**.**

__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__

**,**

**the**discrete sine transform

**is**

**a**linear

**,**invertible

__function__F: R < sup > N </ sup > < tt >-></ tt > R < sup > N </ sup >

**(**where R denotes

**the**set

**of**real numbers

**),**or equivalently an N × N square matrix

**.**

__Formally__

**,**

**the**discrete Hartley transform

**is**

**a**linear

**,**invertible

__function__H: R < sup > n </ sup > < tt >-></ tt > R < sup > n </ sup >

**(**where R denotes

**the**set

**of**real numbers ).

__Formally__

**,**

**a**cardinal κ

**is**defined to be weakly compact if it

**is**uncountable and for every

__function__f: < sup > 2 </ sup > →

__Formally__

**,**an analytic

__function__ƒ

**(**z )

**of**

**the**real or complex variables z < sub > 1 </ sub >,…, z < sub > n </ sub >

**is**transcendental if z < sub > 1 </ sub >, …, z < sub > n </ sub >, ƒ

**(**z ) are algebraically independent

**,**i

**.**e., if ƒ

**is**transcendental over

**the**field C

**(**z < sub > 1 </ sub >, …, z < sub > n </ sub >).

__Formally__

**,**this means that

**,**for some

__function__f

**,**

**the**image f

**(**D )

**of**

**a**directed set D

**(**i

**.**e

**.**

**the**set

**of**

**the**images

**of**each element

**of**D )

**is**again directed and has as

**a**least upper bound

**the**image

**of**

**the**least upper bound

**of**D

**.**One could also say that f preserves directed suprema

**.**

__Formally__

**,**let be

**a**stochastic process and let represent

**the**cumulative distribution

__function__

**of**

**the**joint distribution

**of**at times

**.**

__Formally__

**,**an ultrametric space

**is**

**a**set

**of**points with an associated distance

__function__

**(**also called

**a**metric )

0.135 seconds.