Instead, they are governed by wavefunctions that give the probability of finding a particle at each position.

Instead, there is a range of possible observations, each with a different probability.

Instead, it makes a prediction using a probability distribution ; that is, it describes the probability of obtaining the possible outcomes from measuring an observable.

Instead, the conclusion of an inductive argument follows with some degree of probability.

Instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.

Instead of probability estimates they simply define maximum levels of acceptable loss for each.

Instead, the organism records the times of onset and offset of CSs and USs and uses these to calculate the probability that the US will follow the CS.

Instead, due to sensitivity to initial conditions, unstable systems can only be explained statistically, that is, in terms of probability.

Instead, armed with a value for the planet, we can put in place systems that provide early warning and a good measure of the probability of asteroid impact.

Instead of dealing with only one possible reality of how the process might evolve under time ( as is the case, for example, for solutions of an ordinary differential equation ), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions.

Instead, due to sensitivity to initial conditions, unstable systems can only be explained statistically, that is, in terms of probability.

It turns out that in a complete market with no arbitrage opportunities there is an alternative way to do this calculation: Instead of first taking the expectation and then adjusting for an investor's risk preference, one can adjust, once and for all, the probabilities of future outcomes such that they incorporate all investors ' risk premia, and then take the expectation under this new probability distribution, the risk-neutral measure.

Instead, the correct calculation uses Bayes ' theorem to take into account the prior probability of any randomly selected inhabitant in the city being a terrorist and the total probability of the bell ringing:

Instead the hidden variable set at the source is taken to determine only the probability of a given outcome, the actual individual outcomes being partly determined by other hidden variables local to the analyser and detector.

Instead of taking the max or min of the utility values of their children, chance nodes take a weighted average, with the weight being the probability that that child is reached.

Instead of generating sample paths randomly, it is possible to systematically ( and in fact completely deterministically, despite the " quasi-random " in the name ) select points in a probability spaces so as to optimally " fill up " the space.

Instead, the unique Nash equilibrium of this game is in mixed strategies: each player chooses heads or tails with equal probability.

Instead, the above quasiprobability Wigner distribution plays an analogous role, but does not satisfy all the properties of a conventional probability distribution ; and, conversely, satisfies boundedness properties unavailable to classical distributions.

Instead one may find the probability of the complementary event and subtract it from 1, thus:

Instead of forcing the diffusion anisotropy data into a group of tensors, the mathematics used deploys both probability distributions and a classic bit of geometric tomography and vector math developed nearly 100 years ago — the Funk Radon Transform.

Instead losses mounted, from £ 68 million in 1960 to £ 87 million in 1961, and £ 104 million in 1962.

Instead, losses at the newsweekly accelerated: revenue dropped 38 percent from 2007 to 2009.

Instead of wins and losses, competitors are awarded " ups " ( for being in the top half of the room ) and " downs " ( for being in the bottom half of the room ).

Instead, they arranged the National Transportation Act that agreed to pay 80 % of any losses.

Instead, the division was strung out on the Zolochiv-Zboriv section of the Lviv-Ternopil road, and suffered immense losses from Red Air Force Il-2s.

Instead, the corporation's income or losses are divided among and passed through to its shareholders.

Instead of giving themselves spontaneously to the orgiastic release that jazz can give them, they undergo psychoanalysis or flirt with mysticism or turn to prostitutes for satisfaction.

Instead of radiators you'll have cooling-heating units, each with its own thermostat.

Instead, he constantly became lost in parts and components of them, confused some of their details with those of neighboring objects, and so on, unless he allowed time to `` trace '' the object in question through minute movements of the head and hands and in this way to discover its contours.

Instead of isolating the literal flatness by specifying and circumscribing it, the pasted paper or cloth releases and spreads it, and the artist seems to have nothing left but this undepicted flatness with which to finish as well as start his picture.

Instead he brought with him the names of some people he had never met and of whom the medium knew nothing.

Instead, the audience can sit back at ease and, from the perspective of an enlightened time which no longer believes in such things, enjoy the dead seriousness with which the characters in the play take the witches and devils which are under discussion.

Instead of linking the nine numbers of this diagram with the traditional Nine Provinces, as was usually done, this equated the odd, Yang numbers with mountains ( firm and resistant, hence Yang ) and the even numbers with rivers ( sinuous and yielding, hence Yin ) ; ;

Instead -- and not just to prove my objectivity -- I hasten to report that it's a highly amusing film which probably does a fairly accurate job of reporting on the Easter vacation shenanigans of collegians down in Fort Lauderdale, and that it seems to come to grips quite honestly with the moral problem that most commonly vexes youngsters in this age group -- that is to say, sex.

Instead the cartoons seem to deal with foibles.

Instead of having a pulp cavity, each tooth has a cluster of thin, upright, parallel tubes of vasodentin ( a modified form of dentine ), with individual pulp canals, held together by cementum.

Instead of starting from theory and applying theory to a particular case, casuists start with the particular case itself and then ask what morally significant features ( including both theory and practical considerations ) ought to be considered for that particular case.

Instead, the irrigated agriculture project was headed for completion with apparently no prospects for extension beyond 2011.

Instead, Rufinus attempted to negotiate with Alaric in person, which only aroused suspicions in Constantinople that Rufinius was in league with the Goths.

Instead, that night ( July 17 / 18 ), Alexios III hid in the palace, and finally, with one of his daughters, Eirene, and such treasures ( 1, 000 pounds of gold ) as he could collect, got into a boat and escaped to Debeltos in Thrace, leaving his wife and his other daughters behind.

Instead of just establishing it as a military prison, he provided for a civil administration, with courts of law.

Instead, AMOS BASIC controlled the computer directly, which caused programs written in it to have a non-standard user interface, and also caused compatibility problems with newer versions of the operating system.

Instead of using Vermin's tired characters, Abner inventively peopled the strip with hillbillies.

Since the 2002 edition, the Apostles ' Creed is included in the Roman Missal with the indication, " Instead of the Niceno-Constantinopolitan Creed, especially during Lent and Easter time, the baptismal Symbol of the Roman Church, known as the Apostles ’ Creed, may be used.

Instead of reviewing music videos, they reviewed ( custom-made ) pages from other Marvel Comics — in one with Ghost Rider, Beavis tries to avoid using the word " fire " to describe the character's fiery skull.

Instead, space itself expands with time everywhere and increases the physical distance between two comoving points.

Instead, it is put in parallel with chapter 4 ( C ) where divine judgements are pronounced against the Babylonian kings.

Instead, the Hebrew name Ahasuerus accords with an inscription of the time that notes that Artaxerxes II was named also Arshu, understood as a shortening of Achshiyarshu the Babylonian rendering of the Persian Khshayarsha ( Xerxes ), through which the Hebrew Achashverosh ( Ahasuerus ) is derived.