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Page "Independence (probability theory)" ¶ 25
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Two and random
Two principal methods are used for this: chromosome walking, which progresses through the entire strand, piece by piece, and shotgun sequencing, which is a faster but more complex process, and uses random fragments.
Two random variables that are normally distributed may fail to be jointly normally distributed, i. e., the vector whose components they are may fail to have a multivariate normal distribution.
Two such discriminated " warning bells " are widely understood: green-flashing, random triangles appearing on the screen usually correspond to overheating problems on the GPU itself, while white, flashing dots appearing randomly ( usually in groups ) on the screen often mean that the card's RAM is overheating.
Two adsorbate nitrogen molecules adsorbing onto a tungsten adsorbent from the precursor state around an island of previously adsorbed adsorbate ( left ) and via random adsorption ( right )
Two random examples of jokes are, " I once spent an evening with seven Benedictines.
* May 2005-August 2006: Two men in Phoenix, AZ ( dubbed " Serial Shooter " by the media ), Dale Hausner and Samuel Dieteman, went on a year-long random shooting spree.
Two random variables X and Y are conditionally independent given a third random variable Z if and only if they are independent in their conditional probability distribution given Z.
Two random variables X and Y are conditionally independent given a σ-algebra Σ if the above equation holds for all R in σ ( X ) and B in σ ( Y ).
Two random variables X and Y are conditionally independent given a random variable W if they are independent given σ ( W ): the σ-algebra generated by W. This is commonly written:
Two people from each district pool, one man and one woman, were selected by random draw for membership in the Citizens ’ Assembly.
Two times out of ten the result will truncate back to 4 ( if 0. 0 or 0. 1 are added to 4. 8 ) and the rest of the times it will truncate to 5, but each given situation has a random 20 % chance of rounding to 4 or 80 % chance of rounding to 5.
Two examples of aggregates generated using a microcomputer by allowing random walkers to adhere to an aggregate ( originally ( i ) a straight line consisting 1300 particles and ( ii ) one particle at center ) are shown on the right.
Two months later, at Slamboree 1996, The Barbarian and Meng were on opposing teams in a " Lethal Lottery " tournament that saw partners supposedly chosen at random.
Two reports of Anderson localization of light in 3D random media exist up to date ( Wiersma et al., 1997 and Storzer et al., 2006 ; see Further Reading ), even though absorption complicates interpretation of experimental results ( Scheffold et al., 1999 ).
Two players, one usually a returning champion, competed in a three-round game where the object was to guess the definitions of any of nine random words displayed on a screen, arranged in a 3-by-3 grid with the middle row of the grid raised one level above the others.
Two follow-up works appeared the next year in CRYPTO 2008, giving definitional equivalences and constructions without random oracles,.

Two and variables
Two terms with the same variables raised to the same powers are called " similar terms " or " like terms ", and they can be combined, using the distributive law, into a single term whose coefficient is the sum of the coefficients of the terms that were combined.
Walden Two embraces the proposition that the behavior of organisms, including humans, is determined by genetic and environmental variables, and that systematically altering environmental variables can generate a sociocultural system that very closely approximates utopia.
Two variables move in the opposite direction.
Two expressions are said to be equivalent if, for each combination of values for the free variables, they have the same output, i. e., they represent the same function.
Two structures M and N of the same signature σ are elementarily equivalent if every first-order sentence ( formula without free variables ) over σ is true in M if and only if it is true in N, i. e. if M and N have the same complete first-order theory.
Two leading marketing texts differ slightly on which variables are the most important, with Dibb, Simkin, Pride and Ferrell ( p676 ) identifying:
Two generally true circumstances underlie the theory of thoughtful, therapeutic polypharmacy: ( 1 ) Drugs given for a single somatic locale act on biochemical mechanisms present throughout the body such that their nonlinear interactions can produce an ( unknown except empirically ) global physiological state of health ;( 2 ) The more independent variables, " handles ", to manipulate, the greater the likelihood of finding and stabilizing a small available parametric space of healthy function while minimizing unwanted effects.
Two variables are perfectly collinear if there is an exact linear relationship between the two.
Two integral forms are called equivalent if there exists an invertible integral linear change of variables that transforms the first form into the second.

Two and X
Two years later, Fate magazine published " Sea Mystery at Our Back Door ", a short article by George X.
* Two compact Hausdorff spaces X < sub > 1 </ sub > and X < sub > 2 </ sub > are homeomorphic if and only if their rings of continuous real-valued functions C ( X < sub > 1 </ sub >) and C ( X < sub > 2 </ sub >) are isomorphic.
Sometimes used as a symbol for Christian marriage: Two gold wedding rings interlinked with the Greek letters Chi ( letter ) | chi ( X ) and Rho ( letter ) | rho ( P )— the first two letters in the Greek word for " Christ " ( see Labarum )
Two members of the family, were popes as Leo X and Clement VII in the early 16th century.
where n is a natural number, the coefficients are elements of R, and X is a formal symbol, whose powers X < sup > i </ sup > are just placeholders for the corresponding coefficients a < sub > i </ sub >, so that the given formal expression is just a way to encode the sequence, where there is an n such that a < sub > i </ sub > = 0 for all i > n. Two polynomials sharing the same value of n are considered equal if and only if the sequences of their coefficients are equal ; furthermore any polynomial is equal to any polynomial with greater value of n obtained from it by adding terms in front whose coefficient is zero.
Other successful titles that followed include BlazBlue: Calamity Trigger, Marvel vs. Capcom 3: Fate of Two Worlds, Mortal Kombat, Super Smash Bros. Brawl, Street Fighter X Tekken, and The King of Fighters XIII.
Two X. 25 hosts could, of course, call one another directly ; no PAD is involved in this case.
Two disjoint closed subsets A and B of a topological space X are said to be separated by neighbourhoods if there are neighbourhoods U of A and V of B that are also disjoint.
Two studies found a prevalence of cardiovascular malformations of 30 % and 38 % in a group of pure 45, X monosomy.
Two of Louis XV's other grandchildren, Louis XVIII and Charles X, would occupy the throne of France after the fall of Napoleon I.
Two manuscripts name him: MS. A ( Avranches MS 162, 12th-century ), refers to Uortigerno ; and Mommsen's MS. X ( Cambridge University Library MS. Ff.
Two of the SBS's four squadrons, C and X, are configured for general operations.
The first significant releases of sequels took place between The Lord of the Rings: The Two Towers, Harry Potter and the Chamber of Secrets, Star Wars Episode II: Attack of the Clones, Men in Black II, Analyze That, Spy Kids 2: The Island of Lost Dreams, Stuart Little 2, Blade II, the 3rd installment Austin Powers in Goldmember, the 10th installments Star Trek Nemesis and Jason X.
Henri was the posthumous son of Charles Ferdinand, Duke of Berry, younger son of Charles X of France, by his wife, Princess Carolina of Naples and Sicily, daughter of King Francis I of the Two Sicilies.
* 1996: X Games Two – Providence & Newport, Rhode Island
Two spaces X and Y are homotopy equivalent if they can be transformed into one another by bending, shrinking and expanding operations.
Two French kings died from tennis-related episodes – Louis X of a severe chill after playing and Charles VIII after striking his head on the lintel of a door leading to the court in Amboise.
Two metric spaces X and Y are called isometric if there is a bijective isometry from X to Y.
Two maps f, g are called homotopic relative to A if they are homotopic by a basepoint-preserving homotopy F: D < sup > n </ sup > × → X such that, for each p in S < sup > n − 1 </ sup > and t in, the element F ( p, t ) is in A.

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