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Note that the probability of risk occurrence is difficult to estimate, since the past data on frequencies are not readily available, as mentioned above.
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Note and probability
Note that the probability of finding particles in the same state is relatively larger than in the distinguishable case.
Note that not every probability distribution has a defined mean ; see the Cauchy distribution for an example.
* The probability a set will have features different and features the same is ( Note: d = 0 all four features the same is impossible as no two cards are identical ).
Note: This is not the same as the probability that those parameters are the right ones, given the observed sample.
Note that the obvious compatibility condition, namely, that this marginal probability distribution be in the same class as the one derived from the full-blown stochastic process, is not a requirement.
Note that what affects the value of for different values of is only the factors and, which both appear in the numerator, and hence the posterior probability is proportional to both.
Note that both types of predictive distributions have the form of a compound probability distribution ( as does the marginal likelihood ).
Note that the Bernstein-von Mises theorem asserts here the asymptotic convergence to the " true " distribution because the probability space corresponding to the discrete set of events is finite ( see above section on asymptotic behaviour of the posterior ).
Note that the ground state probability density is concentrated at the origin.
: Decomposition: Note corresponds to the probability density.
Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it.
Note that both of these are probabilities in a measure theoretic sense, and neither of these is the true probability of expiring in-the-money under the real probability measure.
( Note that some other algorithms may also output confidence values, but in general, only for probabilistic algorithms is this value mathematically grounded in probability theory.
Note that 1 ) many matings are required to have a high probability of detecting a homozygous dominant ( once a ridgeless pup is produced, the animal in question is assumed to be homozygous without question ), and 2 ) more than one sire can produce the pups in one litter.
Note that although we are looking at success / failure, the data are not accurately modeled by the binomial distribution, because the probability of success on each trial is not the same, as the size of the remaining population changes as we remove each marble.
Note that power is the probability of finding a difference that does exist, as opposed to the likelihood of declaring a difference that does not exist ( which is known as a Type I error, or " false positive ").
Note that if the probability density function is a function of various parameters, so too will be its normalizing constant.
Note that the expectation of this random variable is equal to the probability of A itself:
Note that a marginal probability can always be written as an expected value:
Note also that the probability is proportional to the resulting value ; the actual probability must be determined by normalizing across all the possible values that the categorical variable can take ( i. e. adding up the computed result for each possible value of the categorical variable, and dividing all the computed results by this sum ).
Note that gcd ( x, N )= 1 with overwhelming probability, which ensures that there are 4 square roots of x < sup > 2 </ sup > mod N.
Note that this expression is not guaranteed to be positive, and is therefore not a valid probability distribution.
Note and risk
Note that some finance and economic theories assume that market participants can borrow at the risk free rate ; in practice, of course, very few ( if any ) borrowers have access to finance at the risk free rate.
Note that the requirements activity takes place in multiple sections and in multiple iterations, just as planning and risk analysis occur in multiple places.
( Note: Don't use salicylates, like aspirin, for influenza: Increased risk of Reyes Syndrome )
Note however that systematic risk is not due to individual institutions per se, but due to the interconnections.
Note that above, the risk neutral formula does not refer to the volatility of the underlying – p as solved, relates to the risk-neutral measure as opposed to the actual probability distribution of prices.
Note that the theory uses standard deviation of return as a proxy for risk, which is valid if asset returns are jointly normally distributed or otherwise elliptically distributed.
Note, if R < sub > f </ sub > is a constant risk free return throughout the period,
Note that for the purposes of risk management, " to create realistic interest rate simulations ," these Multi-factor short-rate models are sometimes preferred over One-factor models, as they produce scenarios which are, in general, better " consistent with actual yield curve movements ".
Note, however, that more and more return on risk adjusted capital ( RORAC ) is used as a measure, whereby the risk adjustment of Capital is based on the capital adequacy guidelines as outlined by the Basel Committee, currently Basel III.
Note and occurrence
Note that the occurrence of brown recluses in a single building ( such as a warehouse ) outside of the native range is not considered a successful colonization ; such single-building populations can occur ( e. g., several such cases in Florida ), but do not spread, and can be easily eradicated.
Note that this is a regular occurrence for birds, which can get killed in flight, or stunned, and then fall ( unlike flightless creatures, which first have to be lifted into the air by an outside force ).
Note: All episodes are listed chronologically in order of occurrence within the Cramp Twins universe.
Note that the proper terminology for this occurrence includes the letter'd ' at the end of the first word, hence " doubled die ".
* 1840 Note on the occurrence at various times of the bottle-nosed whale ( Hyperoodon butzkoph, Lancep.
Note and is
( Note: So far as State Police cars are concerned, only their replacement is under this division ).
Note, however, that it is six inches shorter at the forward end.
Note another piece of wood six inches wide is fastened to the transom between these pieces.
Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.
Note that the mass threshold is four times that of 1958 Alpha and that the flux is one fifth as large.
Note that the mass scale is one to two orders of magnitude greater than some previously used ; ;
Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.
Note that flexural strength is not always improved by simply increasing the density, nor is the change always proportional from one formulation to another.
Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by
Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.
Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.
Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.
Note that there is no directly corresponding concept in the German language.
Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.
Note that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.
Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.
Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.
Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.
Note that this is subtly different to the ' thanks ' list in the original BBC Model B.
7.078 seconds.