However, if clusters are selected with probability proportionate to size, the same number of interviews should be carried out in each sampled cluster so that each unit sampled has the same probability of selection.

However, consider the short but never halting algorithm which systematically lists and runs all possible programs ; whenever one of them halts its probability gets added to the output ( initialized by zero ).

However, due to Eisenhower's persistence, the pivotal supply port at Antwerp was successfully, albeit belatedly, opened in late 1944, and victory became a more distinct probability.

However, for well-understood faults the probability that a segment may rupture during the next few decades can be estimated.

However, this is not correct, and is a manifestation of the gambler's fallacy ; the event of 5 heads in a row and the event of " first 4 heads, then a tails " are equally likely, each having probability.

However, the probability of flipping a head after having already flipped 20 heads in a row is simply.

However, because close relatives share a large fraction of their alleles, the probability that any such rare deleterious allele present in the common ancestor will be inherited from both related parents is increased dramatically with respect to non-inbred couples.

However, quantum mechanics does not pinpoint the exact values of a particle's position and momentum ( since they are conjugate pairs ) or its energy and time ( since they too are conjugate pairs ); rather, it only provides a range of probabilities of where that particle might be given its momentum and momentum probability.

However, by repeatedly initializing, running and measuring the quantum computer, the probability of getting the correct answer can be increased.

However, the symptom overlap is such that it is impossible to diagnose the type of dementia by symptomatology alone, and in only a few cases are symptoms enough to give a high probability of some specific cause.

However, a diffraction grating can be made out of this mirror, by scraping away areas near the edge of the mirror that usually cancel nearby amplitudes out — but now, since the photons would not reflect from the scraped-off portions, the probability amplitudes which would all wind up pointing, for instance, at forty-five degrees can have a sizable sum.

However, in order to achieve the same bit-error probability as BPSK, QPSK uses twice the power ( since two bits are transmitted simultaneously ).

However, terms become 0 at points where either variable has finite probability density.

However, if the random variable has an infinite but countable probability space ( i. e. corresponding to a die with infinite many faces ) the 1965 paper demonstrates that for a dense subset of priors the Bernstein-von Mises theorem is not applicable.

However, if we attempt to move to a less probable point, we will sometimes reject the move, and the more the relative drop in probability, the more likely we are to reject the new point.

However, the Schrödinger equation predicts that there is a small probability that the ball will get to the other side of the hill, even if it has too little energy to reach the top.

However, the theory is usually applied only when the probability distribution of the next step depends non-trivially on the current state.

This is because < sup > 238 </ sup > U is much more stable than < sup > 235 </ sup > U or < sup > 234 </ sup > U, as the half-life of each isotope reveals: 4. 468 × 10 < sup > 9 </ sup > years for < sup > 238 </ sup > U compared to 7. 038 × 10 < sup > 8 </ sup > years for < sup > 235 </ sup > U and 245, 500 years for < sup > 234 </ sup > U. However, the natural abundance of a given isotope is also affected by the probability of its creation in nucleosynthesis ( as in the case of samarium ; radioactive < sup > 147 </ sup > Sm and < sup > 148 </ sup > Sm are much more abundant than stable < sup > 144 </ sup > Sm ) and by production of a given isotope by natural radioactive isotopes ( as in the case of radiogenic isotopes of lead ).

However, it is also possible for a system to be in a statistical ensemble of different state vectors: For example, there may be a 50 % probability that the state vector is and a 50 % chance that the state vector is.

However, unpolarized light can be described perfectly by assuming that each photon is either with 50 % probability or with 50 % probability.

However, the probability for a complete or partial success is greater than the probability of a complete failure or partial failure.

However, they do demonstrate the presence of large normal pressures in the presence of flat shear fields which were forecast by the theory in the first part of the paper.

However, Montgomery makes little contribution to leadership theory and practice.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

However, this theory is undermined by the disproportional fear of spiders in comparison to other, potentially dangerous creatures that were present during Homo sapiens environment of evolutionary adaptiveness.

However, more vital propositions, such as Hume's argument for the role of habit in a theory of knowledge, are retained.

However, invalid formulas ( those that are not entailed by a given theory ), cannot always be recognized.

However, Davy failed to develop a new theory, concluding that " acidity does not depend upon any particular elementary substance, but upon peculiar arrangement of various substances ".

However, the argument concludes that the conceptual challenge of bare particulars leaves a bundle of properties and nothing more as the only possible conception of an object, thus justifying bundle theory.

However, the results of BCS theory do not depend on the origin of the attractive interaction.

However, since piston-engined aircraft rely upon magnetos to provide spark to their cylinders rather than a battery powered ignition coil system, this theory is not strongly convincing.

However, the term naive set theory is also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory ; care is required to tell which sense is intended.

However, one could equally well lay out a consequentialist theory that focuses solely on minimizing bad consequences.

However it is important to note that the objects of a category need not be sets nor the arrows functions ; any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category, and all the results of category theory will apply to it.

However, the later edition in 1959 failed to adequately address the problems that appeared to be better understood by molecular orbital theory.

However, the work of Friedrich Hund, Robert Mulliken, and Gerhard Herzberg showed that molecular orbital theory provided a more appropriate description of the spectroscopic, ionization and magnetic properties of molecules.

" However, in the case of the so-called Nilo-Hamitic languages ( a concept he introduced ), it was based on the typological feature of gender and a " fallacious theory of language mixture.

However, spectropolarimetric observations of SN 2009dc showed it had a polarization smaller than 0. 3, making the large asphericity theory unlikely.

However it was only in 1927 that the shakta theory of seven main chakras, that has become most popular in the West, was introduced, largely through the translation of two Indian texts: the Sat-Cakra-Nirupana, and the Padaka-Pancaka, by Sir John Woodroffe, alias Arthur Avalon, in a book titled The Serpent Power.

However, control theory also saw an increasing use in fields such as economics.

However, this political restriction is less confining than it may first appear in that the Marxist historical framework is surprisingly flexible, and a rather simple matter to modify an alternative historical theory to use language that at least does not challenge the Marxist interpretation of history.

However this theory ignores the fact that the Soviet Union had already suffered several important setbacks during “ reactive and defensive strategy ” of “ containment ”.

However, unlike Johnson, Hodge confined the term to exclude those like Asa Gray who combined Christian faith with support for Darwin's natural selection theory, before answering the question posed in the book's title by concluding: " It is Atheism.

However, Russell's theory analyses proper names into a logical structure which makes sense of this problem.

However, one of the consequences of Einstein's theory is that there is no possible physical test that can distinguish between a beam of light as a model of a geometrical line and any other physical model.