Given a counterfactual conditional, e. g., ' If there had been a circle on the blackboard then there would have been a triangle ', and the subsequent information ' in fact there was no triangle ', participants make the modus tollens inference ' there was no circle ' more often than they do from an indicative conditional ( Byrne and Tasso, 1999 ).

Given events, and, Bayes ' rule states that the conditional odds of given are equal to the marginal odds of multiplied by the Bayes factor:

Given our current estimate of the parameters θ < sup >( t )</ sup >, the conditional distribution of the Z < sub > i </ sub > is determined by Bayes theorem to be the proportional height of the normal density weighted by τ:

Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value.

Given discrete random variable with support and with support, the conditional entropy of given is defined as:

* Conditional distribution: Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X ( written " Y | X ") is the probability distribution of Y when X is known to be a particular value.

Given the limited amount of good quality agricultural land to begin with, that policy has resulted in continual deforestation and subsequent erosion.

Given the state at some initial time ( t = 0 ), we can solve it to obtain the state at any subsequent time.

" Given the chance to relive his life by switching bodies with " a talentless 20 year-old wannabe rock star with all the looks and charm Rocky used to have ," the series deals with the subsequent soul-searching and reflection over such a decision.

Given the subsequent emergence of organized fandom for comic books among adults who grew up reading them during Comics ' Golden Age, it is ironic Wertham at one point in Seduction ( pp. 89 – 90 ) asserts " I have known many adults who have treasured throughout their lives some of the books they read as children.

Given a Vulcan's life expectancy of approximately 250 years, it is possible that she is still alive at the time of Star Trek: The Original Series and subsequent movies.

Given budgetary constraints permitted the hiring of another writer, Sena, along with his two producers, would then spend another year writing ten subsequent drafts of the script.

Given this and the subsequent emphasis on building strength at the Gazala position for an attack ( which had been forestalled by the Axis offensive ) it is likely that the defences at Tobruk had not been maintained in first rate condition.

Given the present monophyly of the Nearctic species, it is likely that a single migration and subsequent expansion of the population was the foundation of the Nearctic butterflies.

Given the closeness of Diego Rivera to the people involved, and the fact that the painting is said to slightly predate the murder, some consider it to be evidence of Vidali's and Rivera's involvement in Mella's assassination, also related to Rivera's subsequent expulsion from the Mexican Communist Party.

Given Williamson's testimony that Rowe had still been at the bail hostel at this time, this placed Rowe away from the scene and therefore the subsequent crime spree.

Given the avalanche of canon material which has come since the mid-1980s-the television series Star Trek: The Next Generation, Star Trek: Deep Space Nine, Star Trek: Voyager and Enterprise, several subsequent theatrical films and a library of novelisations-FASA's interpretation of Star Trek has largely been forgotten except by a handful of die-hard fans.

Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

Given the conflicting information available, the true identity of his killer may well be lost to history.

" Given a memex, a scholar could create her own knowledge tools as connections within reams of information, share these tools, and use complexes of tools to create yet more sophisticated knowledge that could in turn be deployed toward this work.

Given this information, a timeline of roughly the years 15 – 98 CE can be established for his adult life.

Given the discriminator PARTY TYPE ( which could be individual, partnership, C Corporation, Sub Chapter S Association, Association, Governmental Unit, Quasi-governmental agency ) the two subtype entities are PERSON, which contains individual-specific information such as first and last name and date of birth, and ORGANIZATION, which would contain such attributes as the legal name, and organizational hierarchies such as cost centers.

Given that the probability p is known, past outcomes provide no information about future outcomes.

Given testable information, the maximum entropy procedure consists of seeking the probability distribution which maximizes information entropy, subject to the constraints of the information.

Given the chronological information of the Imennik, Tervel would have died in 715.

Given Weyoun's untrustworthy nature, it is unclear which information should be believed.

Given the preceding information, the knowledge gap hypothesis can be expressed using the following set of related propositions:

Given that manufacturers are regarded as authorities and that most sales do not happen on manufacturer Web sites, best-in-class manufacturers take their best content and enable other retailers or dealers to publish the information on their sites.

Given all this information, the probability of the observer having spotted a girl given that the observed student is wearing trousers can be computed by substituting these values in the formula:

The prime mechanism then appeared to be this: Given a space X carrying a vector bundle, that implied in the homotopy category a mapping from X to a classifying space BG, for the relevant linear group G. For the homotopy theory the relevant information is carried by compact subgroups such as the orthogonal groups and unitary groups of G. Once the cohomology H *( BG ) was calculated, once and for all, the contravariance property of cohomology meant that characteristic classes for the bundle would be defined in H *( X ) in the same dimensions.

Given that the Pauline epistles are generally dated to AD 50 to AD 60, they are the earliest surviving Christian texts that include information about Jesus.

Given only one share, a second share can be crafted to reveal any possible image ; therefore, individual shares reveal no information about the original image.

Given t-1 shares, no information whatsoever can be determined about the secret.

Given two random variables X and Y whose joint distribution is known, the marginal distribution of X is simply the probability distribution of X averaging over information about Y.

Given the value of p, and no other information relevant to the question of whether the sun will rise tomorrow, the probability that the sun will rise tomorrow is p. But we are not " given the value of p ".

Given the example above, the two galaxies in question cannot have shared any sort of information ; they are not in " causal contact ".

Given this conflicting information, excluding oats appears to be the only risk-free practice for celiac disease sufferers of all ages.

Given Bernal's Marxist and pro-Soviet sympathies it is perhaps remarkable that there has never been any suggestion that he fed any information in that direction.

Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

Given the first four rolls turn up heads, the probability that the next toss is a head is in fact,

Given its limitations, however, NAALC has not produced ( and in fact was not intended to achieve ) convergence in employment, productivity and salary trend in North America.

Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.

Given the above fact, one can ask:

Given that assumption, the evidence for the one-seed theory is the fact that a woman can conceive without coming to orgasm ( though this was still a matter of dispute in the ancient world and the Middle Ages ).

Given the fact that many of the royal depictions of Akhenaten often featured such an elongated head, it is likely an exaggeration of a family trait, rather than a distinct abnormality.

Given any vector space V over K we can construct the tensor algebra T ( V ) of V. The tensor algebra is characterized by the fact:

Given the fact that the period P of an object in circular orbit around a spherical object obeys

Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.

" Given the fact that it's the third film in the series, you couldn't just end with them obtaining the object.

Given Switzerland's particularly strong opinions on who is " Swiss " and who is " other ", it is easy to see that groups such as Stoffunita make use of the fact that hip hop " is still considered a voice for the oppressed " as hip hop scholar and author Jeff Chang notes.

Given on 16 October 1732, they amounted only to recreating his first expedition, but with the added task of heading east and finding North America ( a feat which had in fact just been completed by Mikhail Gvozdev, though this was not known at the time ).

Given parallel morphisms f and g, the equaliser of f and g is just the kernel of g − f, if either exists, and the analogous fact is true for coequalisers.

Given the fact that it was an election year, whose outcome might have changed as a result of a pre-election-day economic downturn, the Bank of Mexico decided to buy Mexican Treasury Securities in order to maintain the monetary base, and thus prevent the interest rates from rising.

Given the fact that the Lakeport area has an economy that is based somewhat on agricultural activities occurring in the Big Valley and Scotts Valley area which involve the growing and harvesting of food and nut crops as well as the increasing wine industry, there are a significant number of transient and seasonal farm workers.

Given the extent and central location of his original holding from the Mill Seat Tract, and the fact that most of the town's pre-1944 building lots are to, Bare's ability to shape the size and extent of development in Roaring Spring was substantial.

Given the fact that the following Popes John, from John XV ( 985 – 996 ) until John XIX ( 1024 – 1034 ), seemed to have neglected the existence of John XIV " bis ", Petrus Hispanus meant to correct this error by electing for himself the name John XXI.

Dr. Tennison states: " Given the account of Elliot Paul, and given that Lead Belly witnessed boogie-woogie in 1899 in the Arklatex ; and given the North to South migration of the Thomas family ; and given the Texas & Pacific headquarters in Marshall in the early 1870s ; and given that Harrison County had the largest slave population in the state of Texas ; and given the fact that the best-documented and largest-scale turpentine camps in Texas did not occur until after 1900 in Southeast Texas, it is most probable that boogie-woogie spread from Northeast to Southeast Texas, rather than from Southeast to Northeast Texas, or by having developed diffusely with an even density over all of the Piney Woods of East Texas.

Given the character's unprecedented popularity and the fact that his name was partially derived from the Latin word for " lucky ", some rather notable individuals and organizations adopted Felix as a mascot.

Given the morphological distinctness of the Cape Verde birds and the fact that the Cape Verde population was isolated from other populations of Red Kites, it cannot be conclusively resolved at this time whether the Cape Verde population was not a distinct subspecies ( as M. migrans fasciicauda ) or even species that frequently absorbed stragglers from the migrating European populations into its gene pool.

Given Juwayni's polemical aims, and the fact that he burned the Ismaili libraries which may have offered much more reliable testimony about the history, scholars have been dubious about his narrative but are forced to rely on it given the absence of alternative sources.

Given the epidemic proportions of obesity in the Western world, and the fact that it is increasing rapidly in some poorer countries, observers expect developments in this area to snowball in the near future.

Given the fact that Puerto Rico has 78 municipalities, there was enough material to show and research over the program's six-year run.