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When and probability
When three dice are tossed repeatedly, what is the probability that the number of aces is 0 ( or 1, or 2, or 3 )??
When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.
When more electrons are added to a single atom, the additional electrons tend to more evenly fill in a volume of space around the nucleus so that the resulting collection ( sometimes termed the atom ’ s “ electron cloud ” ) tends toward a generally spherical zone of probability describing where the atom ’ s electrons will be found.
When the probability of different events is not independent, the probability of future events can change based on the outcome of past events ( see statistical permutation ).
When the probability of repeated events are not known, outcomes may not be equally probable.
When we perform the experiment, the probability of obtaining two particles in the state is now 0. 33 ; the probability of obtaining two particles in the state is 0. 33 ; and the probability of obtaining one particle in the state and the other in the state is 0. 33.
When a coin is fair, that is, the probability of heads is the same as the probability of tails, the entropy of a coin toss is as high as it could be.
When is a conditional probability distribution and the loss function is the negative log likelihood:, then empirical risk minimization is equivalent to maximum likelihood estimation.
When either randomness or uncertainty modeled by probability theory is attributed to such errors, they are " errors " in the sense in which that term is used in statistics ; see errors and residuals in statistics.
When dealing with experiments that are random and well-defined in a purely theoretical setting ( like tossing a fair coin ), probabilities describe the statistical number of outcomes considered divided by the number of all outcomes ( tossing a fair coin twice will yield HH with probability 1 / 4, because the four outcomes HH, HT, TH and TT are possible ).
When it comes to practical application, however, the word probability does not have a singular direct definition.
When studying axiomatic probability theory, many deep consequences follow from merely these three axioms.
When we measure this qubit in the standard basis, the probability of outcome is and the probability of outcome is.
When a statistical procedure has been specified in the study protocol, then statistical theory provides well-defined probability statements for the method when applied to all populations that could have arisen from the randomization used to generate the data.
When the stereochemistry of a macromolecule is considered to be a Bernoulli process, triad composition can be calculated from the probability of finding meso diads ( P < sub > m </ sub >).
When this probability is 0. 25 then the probability of finding:
When we consider 100 billion monkeys, the probability falls to 0. 17 %, and as the number of monkeys n increases, the value of X < sub > n </ sub > – the probability of the monkeys failing to reproduce the given text – approaches zero arbitrarily closely.

When and is
When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.
When they express themselves it is incandescent hatred that shines forth, the rage of repudiation, the ecstasy of negation.
When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.
When the proprietor dies, the establishment should become a corporation until it is either acquired by another proprietor or the government decides to drop it.
When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.
When I take over Taliesin, the first thing I'll do is fire you ''.
When someone in the audience rose and asked how does it feel to be a celebrity, Carl said, `` A celebrity is a fellow who eats celery with celerity ''.
When decision makers act within this frame they determine whether a claim put forward in the name of religion is to be accepted by the larger community as appropriate to religion.
When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.
When we turn to Aristotle's ideas on the moral measure of literature, it is at once apparent that he is at times equally concerned about the influence of the art.
When their faith in civil liberties is tested against strong pressures of social expediency in specific issues, e.g., suppression of `` dangerous ideas '', many waver and give in.
There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.
When I first came across Samuel Johnson's pronouncement, `` the remedy for the ills of life is palliative rather than radical '', it seemed to me to sum up the profoundest of political and social truths.
When all else fails, it is argued that open sessions slow down governmental operations.
When a person has thoughtlessly or deliberately caused us pain or hardship it is not always easy to say, `` Just forget it ''.
When a person meets God's requirements for the experience of forgiveness he is forgiven.
When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.
When different colors are used, she is just as likely to color trees purple, hair green, etc..
When we become firm enough to stand for those ideals which we know to be right, when we become hard enough to refuse to aid nations which do not permit self-determination, when we become strong enough to resist any more drifts towards socialism in our own Nation, when we recognize that our enemy is Communism not war, and when we realize that concessions to Communists do not insure peace or freedom, then, and only then will we no longer be `` soft ''.
When one powerful nation strives to emulate the success of another, it is only natural.
When a man is laid to rest, he is entitled to stay put.
When I talked to Ching about it, he said, Everyone can learn, if he is not a Reactionary or lazy.

When and derived
When values of temperature derived with this instrument were compared with the accepted values associated with liquid helium-4 vapor pressures, differences of about 10 and 7 millidegrees respectively were found.
When derived from natural resins it is most often created out of labdanum.
When the centrifugal force term is expressed in terms of parameters of the rotating frame, replacing with, it can be seen that it is the same centrifugal force previously derived for rotating reference frames.
When the evolution map Φ < sup > t </ sup > ( or the vector field it is derived from ) depends on a parameter μ, the structure of the phase space will also depend on this parameter.
When Greek orthography was codified by grammarians in the Hellenistic era, they used a diacritic symbol derived from this half-H shape to signal the presence of / h /, and added as its counterpart a reverse-shaped diacritic to denote absence of / h /.
When synchronizing multiple clock-dependent digital devices together with video, such as digital audio recorders, the devices must be connected to a common word clock signal that is derived from the house black burst signal.
When used with a 68020 bus, the 68030 did not differentiate itself in performance from the 68020 that it was derived from.
" David Gordon notes, " When most people speak of natural law, what they have in mind is the contention that morality can be derived from human nature.
When Archbishop Emmanuel Milingo conferred episcopal ordination on four men in Washington on September 24, 2006, the Holy See's Press Office declared that " the Church does not recognize and does not intend in the future to recognize these ordinations or any ordinations derived from them, and she holds that the canonical state of the four alleged bishops is the same as it was prior to the ordination.
When geologist Henry De la Beche painted Duria Antiquior, the first widely circulated pictorial representation of a scene from prehistoric life derived from fossil reconstructions, he based it largely on fossils Anning had found, and sold prints of it for her benefit.
When the gap is sufficiently wide, real estate developers, landlords, and other people with vested interests in the development of land perceive the potential profit to be derived from re-investing in inner-city properties and redeveloping them for new tenants.
When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated here:
When Pausanias visited the city of Triteia in the second century CE, he was told that the name of the city was derived from an eponymous Triteia, a daughter of Triton, and that it claimed to have been founded by her son ( with Ares ), one among several mythic heroes named Melanippus (" Black Horse ").
When Kimball Township was set off in 1855, the settlement by which Clyde Township derived its name became part of a different township.
When Kimball Township was set off in 1855, the settlement by which Clyde Township derived its name became part of a different township ; a fact with reportedly greatly disappointed Ralph Wadhams.
When the depot was built, the name was changed to " Quamba ," which according to the railway officials was derived from an Indian word for " mudhole "; most likely the name derives from the Ottawa word: zhash < u > kwiimbaa </ u > kmigaa ( fully vocalized as azhashki-wiimbaakamigaa: " be a muddy hole in the ground ").
When served with a layer of fried noodles ( either yakisoba or udon ), the resulting dish is called, the name of which may be derived from the English word " modern " or as a contraction of, meaning " a lot " or " piled high " signifying the volume of food from having both yakisoba and udon.
* When random bits are requested, return that many bits derived from the entropy pool ( by a cryptographic hash function, say ) and decrement the estimate of the number of random bits remaining in the pool.
The long s was derived from the old Roman cursive medial s. When the distinction between upper case ( capital ) and lower case ( small ) letter-forms became established, towards the end of the eighth century, it developed a more vertical form.
When, however, the triglyceride is derived from short chain fatty acids, the released carboxylic acid can confer strong flavors and odors.
When Lord Wemyss criticised the Bill as " strangling the spirit of independence and the self-reliance of the people, and destroying the moral fibre of our race in the anaconda coils of state socialism ", Salisbury responded: " Do not imagine that by merely affixing to it the reproach of Socialism you can seriously affect the progress of any great legislative movement, or destroy those high arguments which are derived from the noblest principles of philanthropy and religion ".
When the object in question is not derived from a class, but from a prototype instead, the size of an object is usually that of the internal data structure ( a hash for instance ) that holds its slots.
" When his father died, his family was left a large trust fund, although de Botton says his income is derived solely from the proceeds of his book sales.
* When the two audio channels are added together, or summed ( L + R plus L-R ), the left channel is derived.
* When the second audio channel is subtracted from the first by a phase reversal ( L + R minus L-R ), the right channel is derived.

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