This implies that expectation values of observables are real.

In probability theory, the expected value ( or expectation, or mathematical expectation, or mean, or the first moment ) of a random variable is the weighted average of all possible values that this random variable can take on.

Habitus refers to lifestyle, the values, the dispositions and expectation of particular social group which are acquired through the activities and experiences of everyday life.

He wrote approvingly of the ideals of democracy and humanitarianism, and his expectation that these values would come to permeate Japanese society.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

We see this reflects the definition of quantum states in general: A quantum state is a mapping from the observables to their expectation values.

that is, the expectation value of A for the mixed state is the sum of the expectation values of A for each of the pure states, weighted by the probabilities p < sub > i </ sub >.

making the expectation values of the kinetic and potential terms above satisfy

Interest on these loans was rolled up, in the expectation that the growth in land values caused by the development of the town would eventually allow the loans to be repaid in full.

For details and examples on how quantum mechanical operators act on the wave function, commutation of operators, and expectation values of operators ; see Operator ( physics ).

This allows the expectation values of and to be easily evaluated for a state.

Virtual particles can be thought of as coming into existence as quantities, such as the electric field, which fluctuate around their expectation values as required by quantum mechanics.

Interest on these loans was rolled up, in the expectation that the growth in land values caused by the development of the town would eventually allow the loans to be repaid in full.

In 1769, in a letter to Benjamin Franklin, he wrote some observations on the expectation of lives, the increase of mankind, and the population of London, which were published in the Philosophical Transactions of that year ; in May 1770 he presented to the Royal Society a paper on the proper method of calculating the values of contingent reversions.

* Arthur Wightman: Quantum field theory in terms of vacuum expectation values.

The fact that the system does not have a unique energy means that the various thermodynamical quantities must be defined as expectation values.

In particular, a martingale is a sequence of random variables ( i. e., a stochastic process ) for which, at a particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value even given knowledge of all prior observed values at a current time.

The vacuum state or is the state of lowest energy and the expectation values of and vanish in this state:

Thus it is easy to see that the expectation values of these field operators vanishes in the vacuum state:

However, it can be shown that the expectation values of the square of these field operators is non-zero.

( The error term does not get included in the expectation values as it is assumed that it satisfies the usual OLS conditions, i. e., E ( U < sub > i </ sub >)

This is because E ( k ) can have any sign whatsoever, and the combination of creation and annihilation operators has expectation value 1 or 0.

The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alters the vacuum expectation value of the energy of the second quantized electromagnetic field.

Resective surgery can be considered palliative if it is undertaken with the expectation that it will reduce but not eliminate seizures.

The actions, attitudes, and relationships of the dominant and subordinate individuals constitute components of role behavior that can vary widely in form, style, and content, but do not vary in the expectation of obedience by the one of superior status, and willingness to obey from the subordinate.

Braid can be taken to imply, in later writings, that hypnosis is largely a state of heightened suggestibility induced by expectation and focused attention.

Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and you can expect to win less money on average than it costs to call the bet.

Perception is not the passive receipt of these signals, but can be shaped by learning, memory and expectation.

Criminal voyeurism statutes are related to invasion of privacy laws but are specific to unlawful surreptitious surveillance without consent and unlawful recordings including the broadcast, dissemination, publication, or selling of recordings involving places and times when a person has a reasonable expectation of privacy and a reasonable supposition they are not being photographed or filmed by " any mechanical, digital or electronic viewing device, camera or any other instrument capable of recording, storing or transmitting visual images that can be utilized to observe a person.

The other common quotation attributed to Yamamoto predicting the future outcome of a naval war against the United States is: " I can run wild for six months … after that, I have no expectation of success ".

The expectation value of the PER is denoted packet error probability p < sub > p </ sub >, which for a data packet length of N bits can be expressed as

It is shown that noisy deviations in the memory-based information processes that convert objective evidence ( observations ) into subjective estimates ( decisions ) can produce regressive conservatism, the conservatism ( Bayesian ), illusory correlations, better-than-average effect and worse-than-average effect, subadditivity effect, exaggerated expectation, overconfidence, and the hard – easy effect.

One can take the expectation of a quadratic form in the random vector X as follows:

One can take the expectation of the product of two different quadratic forms in a zero-mean Gaussian random vector X as follows:

Accommodation can be understood as the mechanism by which failure leads to learning: when we act on the expectation that the world operates in one way and it violates our expectations, we often fail, but by accommodating this new experience and reframing our model of the way the world works, we learn from the experience of failure, or others ' failure.

Nevertheless, there is a unique operator ρ such that the expectation value of F ( A ) can be written as

The expectation value of the measurement can be calculated by extending from the case of pure states ( see Measurement in quantum mechanics ):

Because placebos are dependent upon perception and expectation, various factors that change the perception can increase the magnitude of the placebo response.

The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.

On the other hand, prose poetry can be identified primarily as prose for its reliance on prose's association with narrative and on the expectation of an objective presentation of truth.

He insisted that psychological techniques should always be tried first, for example " even where a violent and destructive maniac could be calmed by a single dose of an antispasmodic referred to opium, observation teaches that in a great number of cases, one can obtain a sure and permanent cure by the sole method of expectation, leaving the insane man to his tumultuous excitement ... ... and seeing, again and again, the unexpected resources of nature left to itself or wisely guided, has rendered me more and more cautious with regard to the use of medications, which I no longer employ — except when the insufficiencies of psychological means have been proven.

More sophisticated MCMC-based algorithms such as coupling from the past can produce exact samples, at the cost of additional computation and an unbounded ( though finite in expectation ) running time.