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Formally, the mutual information of two discrete random variables X and Y can be defined as:

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## Some Related Sentences

Formally and information

__Formally__speaking

**,**a collation method typically defines a total order on a set

**of**possible identifiers

**,**called sort keys

**,**which consequently produces a total preorder on

**the**set

**of**items

**of**

__information__( items with

**the**same identifier are not placed in any

**defined**order ).

__Formally__

**,**knowing

**the**step response

**of**a dynamical system gives

__information__on

**the**stability

**of**such a system

**,**

**and**on its ability to reach one stationary state when starting from another.

Formally and two

__Formally__

**,**

**the**Congress serves

__two__functions

**:**to approve changes to

**the**Party constitution regarding policy

**and**to elect a Central Committee

**,**about 300 strong.

__Formally__

**,**these failed when they were rejected by

**the**Church

**of**England's General Synod in 1972 ; conversations

**and**co-operation continued

**,**however

**,**leading in 2003 to

**the**signing

**of**a covenant between

**the**

__two__churches.

__Formally__

**,**we start with a category C with finite products ( i. e. C has a terminal object 1

**and**any

__two__objects

**of**C have a product ).

__Formally__

**,**this means symmetry under a sub-group

**of**

**the**Euclidean group

**of**isometries in

__two__or three dimensional Euclidean space.

__Formally__

**,**EMF is classified

**as**

**the**external work expended per unit

**of**charge to produce an electric potential difference across

__two__open-circuited terminals.

__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__

**,**

__two__

**variables**are inversely proportional ( or varying inversely

**,**or in inverse variation

**,**or in inverse proportion or in reciprocal proportion ) if one

**of**

**the**

**variables**is directly proportional with

**the**multiplicative inverse ( reciprocal )

**of**

**the**other

**,**or equivalently if their product is a constant.

(

__Formally__speaking**,**this then satisfies**the**premises**of**an axiom**of**well-founded induction**,**which asserts that these__two__conditions are sufficient for**the**proposition to hold for all x.__Formally__

**,**it is a norm

**defined**on

**the**space

**of**bounded linear operators between

__two__given normed vector spaces.

__Formally__

**,**a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra

**,**or superalgebra

**,**over a commutative ring ( typically R or C ) whose product

**,**called

**the**Lie superbracket or supercommutator

**,**satisfies

**the**

__two__conditions ( analogs

**of**

**the**usual Lie algebra axioms

**,**with grading ):

__Formally__

**,**

**the**poem

**can**

**be**understood

**as**

**the**combination

**of**

__two__sonnets

**,**though

**the**spacing

**of**

**the**stanzas is irregular.

__Formally__

**,**given

__two__categories C

**and**D

**,**an equivalence

**of**categories consists

**of**a functor F

**:**C → D

**,**a functor G

**:**D → C

**,**

**and**

__two__natural isomorphisms ε

**:**FG → I < sub > D </ sub >

**and**η

**:**I < sub > C </ sub >→ GF.

__Formally__

**,**a vertex cover

**of**a graph G is a set C

**of**vertices such that each edge

**of**G is incident to at least one vertex in C. The set C is said to cover

**the**edges

**of**G. The following figure shows examples

**of**vertex covers in

__two__graphs (

**and**

**the**set C is marked with red ).

__Formally__

**,**given

__two__partially ordered sets ( S

**,**≤)

**and**( T

**,**≤), a function f

**:**S → T is an order-embedding if f is both order-preserving

**and**order-reflecting

**,**i. e. for all x

**and**y in S

**,**one has

__Formally__

**,**he says

**,**

**the**piece consists

**of**

__two__parts

**of**nearly equal length

**,**

**the**end

**of**

**the**first section being bars 24 – 28 ( p. 77 ).

__Formally__

**,**given a finite set

**X**

**,**a collection C

**of**subsets

**of**

**X**

**,**all

**of**size n

**,**has Property B if we

**can**partition

**X**into

__two__disjoint subsets

**Y**

**and**Z such that every set in C meets both

**Y**

**and**Z.

__Formally__known

**as**" Brooks Institute

**of**Photography ," Brooks Institute offers four majors

**,**

__two__certificate programs

**and**

__two__graduate programs.

Formally and discrete

__Formally__stated

**,**

**the**FFT is a method for computing

**the**

__discrete__Fourier transform

**of**a sampled signal.

__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__

**,**

**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 frieze group is a class

**of**infinite

__discrete__symmetry groups for patterns on a strip ( infinitely wide rectangle ), hence a class

**of**groups

**of**isometries

**of**

**the**plane

**,**or

**of**a strip.

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 variables

__Formally__

**,**collective noun forms such

**as**“ a group

**of**people ” are represented by second-order

__variables__

**,**or by first-order

__variables__standing for sets ( which are well-defined objects in mathematics

**and**logic ).

__Formally__it is precisely in allowing quantification over class

__variables__α

**,**β

**,**etc., that we assume a range

**of**values for these

__variables__to refer to.

__Formally__

**,**they are partial derivatives

**of**

**the**option price with respect to

**the**independent

__variables__( technically

**,**one Greek

**,**gamma

**,**is a partial derivative

**of**another Greek

**,**called delta ).

__Formally__

**,**a constraint satisfaction problem is

**defined**

**as**a triple

**,**where is a set

**of**

__variables__

**,**is a domain

**of**values

**,**

**and**is a set

**of**constraints.

__Formally__

**,**

**the**outcomes

**Y**< sub > i </ sub > are described

**as**being Bernoulli-distributed data

**,**where each outcome is determined by an unobserved probability p < sub > i </ sub > that is specific to

**the**outcome at hand

**,**but related to

**the**explanatory

__variables__.

__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__

**,**an algebraic function in n

__variables__over

**the**field K is an element

**of**

**the**algebraic closure

**of**

**the**field

**of**rational functions K ( x < sub > 1 </ sub >,..., x < sub > n </ sub >).

__Formally__

**,**propositional models

**can**

**be**represented by sets

**of**propositional

__variables__; namely

**,**each model is represented by

**the**set

**of**propositional

__variables__it assigns to true.

__Formally__

**,**

**the**extension

**of**circumscription that incorporate varying

**and**fixed

__variables__is

**as**follows

**,**where is

**the**set

**of**

__variables__to minimize

**,**

**the**fixed

__variables__

**,**

**and**

**the**varying

__variables__are those not in

**:**

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