We cannot, of course, assign it any substance.

Representable functors: We can generalize the previous example to any category C. To every pair X, Y of objects in C one can assign the set Hom ( X, Y ) of morphisms from X to Y.

The Chinese did assign names to α Tel ( We, meaning danger ), and γ Tel ( the present-day G Scorpii ) as Chuen Shwo, with a mythological meaning.

We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree.

We have very little evidence of the internal working arrangements of the workshop, apart from the works of art themselves, often very difficult to assign to a particular hand.

We arbitrarily assign these the values 1 through 26 for the letters, and 0 for '#'.

We determine the rational part without integrating it and we assign a given integral into Ostrogradsky's form:

" We assign Hainina to the Kogaionidae ( superfamily incertae sedis ); it differs from Kogaionon in having ornamented enamel, while the enamel is smooth in Kogaionon ," ( Kielan-Jaworowska & Hurum, 2001, p. 409 ).

We draw a card from the deck ; applying the principle of indifference, we assign each of the possible outcomes a probability of 1 / 52.

We assign reserves for natives ... indicate ( sites for ) European settlement.

8 Did We not assign unto him two eyes

:... We are not disputing, however, your right to assign channels and set aside bands for the prevention of interference.

We repeat, that the test of a violation of 7 is whether, at the time of suit, there is a reasonable probability that the acquisition is likely to result in the condemned restraints.

We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

We want to study the probability function of this random variable.

We shall find a formula for the probability of exactly X successes for given values of P and N.

We can run the algorithm a constant number of times and take a majority vote to achieve any desired probability of correctness less than 1, using the Chernoff bound.

We can see from the above that, if one flips a fair coin 21 times, then the probability of 21 heads is 1 in 2, 097, 152.

We would expect to find the total probability by multiplying the probabilities of each of the actions, for any chosen positions of E and F. We then, using rule a ) above, have to add up all these probabilities for all the alternatives for E and F. ( This is not elementary in practice, and involves integration.

We then have a better estimation for the total probability by adding the probabilities of these two possibilities to our original simple estimate.

We are allowed to keep the Schrödinger expression for the current, but must replace by probability density by the symmetrically formed expression

We obtain the same variation in probability amplitudes by allowing the time at which the photon left the source to be indeterminate, and the time of the path now tells us when the photon would have left the source, and thus what the angle of its " arrow " would be.

We need to stop when the state vector passes close to ; after this, subsequent iterations rotate the state vector away from, reducing the probability of obtaining the correct answer.

We consider a special case of this theorem for a binary symmetric channel with an error probability p.

We use the shorthand notation to denote the joint probability of by.

We can then infer that the probability that it has between 600 and 1400 words ( i. e. within k = 2 SDs of the mean ) must be more than 75 %, because there is less than chance to be outside that range, by Chebyshev ’ s inequality.

We use Lagrange multipliers to find the point of maximum entropy,, across all discrete probability distributions on.

We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory ( measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible — in quantum mechanical terms they always commute ).

We start with the standard assumption of independence of the two sides, enabling us to obtain the joint probabilities of pairs of outcomes by multiplying the separate probabilities, for any selected value of the " hidden variable " λ. λ is assumed to be drawn from a fixed distribution of possible states of the source, the probability of the source being in the state λ for any particular trial being given by the density function ρ ( λ ), the integral of which over the complete hidden variable space is 1.

There is, nevertheless, a small chance that we are unlucky and hit an a which is a strong liar for n. We may reduce the probability of such error by repeating the test for several independently chosen a.

Given the observation space, the state space, a sequence of observations, transition matrix of size such that stores the transition probability of transiting from state to state, emission matrix of size such that stores the probability of observing from state, an array of initial probabilities of size such that stores the probability that. We say a path is a sequence of states that generate the observations.

We separate the case in which the measure space is a probability space from the more general case because the probability case is more accessible for the general reader.

We denote the canonical probability distributions for the Hamiltonian and the trial Hamiltonian by and, respectively.

We can model the electrons at the sheath edge with a Boltzmann distribution, i. e.,

We also give a simple method to derive the joint distribution of any number of order statistics, and finally translate these results to arbitrary continuous distributions using the cdf.

We assume throughout this section that is a random sample drawn from a continuous distribution with cdf.

He said, “ I have been building a brewery with the Celis family .” “ We ’ ve already been building the distribution network ,” he said.

We don't need to assume anything about the distribution of test scores to reason that before we gave the test it was equally likely that the highest score would be any of the first 100.

We then generate a random start from a uniform distribution between 0 and 1, and move along the number line in steps of 1.

CFO Mike Ciskowski stated " We believe the separation of our retail business by way of a tax-efficient distribution to our shareholders will create operational flexibility within the business and unlock value for our shareholders.

We see that exponential decay is a scalar multiple of the exponential distribution ( i. e. the individual lifetime of each object is exponentially distributed ), which has a well-known expected value.

If T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to estimate the expected value θ of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. We then calculate the standard score Z = ( T − θ ) / s, from which one-tailed and two-tailed p-values can be calculated as Φ (−| Z |) and 2Φ (−| Z |), respectively, where Φ is the standard normal cumulative distribution function.

We use cumulative distribution functions ( cdf ) in order to encompass both discrete and continuous distributions.

#: We list the HSPs whose scores are greater than the empirically determined cutoff score S. By examining the distribution of the alignment scores modeled by comparing random sequences, a cutoff score S can be determined such that its value is large enough to guarantee the significance of the remaining HSPs.

< p >“ We are the largest creator and distributor of copyrights in the world, and as the first to deploy the FSN – an entirely new distribution channel – we can now accurately assess the potential for such on-demand programming as movies, sports, news, advertising, shopping, education, games, music and more.

We do not present the model here in detail but we only use its detailed data on income distribution, when the objective functions are formulated in the next section.

We have demonstrated above that the real income change is achieved by quantitative changes in production and the income distribution change to the stakeholders is its dual.

We could specify, say, a normal distribution as the prior for his speed, but alternatively we could specify a normal prior for the time he takes to complete 100 metres, which is proportional to the reciprocal of the first prior.

We use the probability mass function for the Poisson distribution, which tells us that

We can express the expectation value of x by the probability distribution W ( x, 0 ) and the transition probability

We expand in terms of a known distribution with probability density function, characteristic function, and cumulants γ < sub > r </ sub >.

where s = x < sub > 1 </ sub > + ... + x < sub > n </ sub > is the number of " successes " and n is of course the number of trials, and then normalizes, to get the " posterior " ( i. e., conditional on the data ) probability distribution of p. ( We are using capital X to denote a random variable and lower-case x either as the dummy in the definition of a function or as the data actually observed.

We, who recognize the needs and aspirations of the Filipino masses, with the aid of Divine Providence, in order to establish a society enjoying full political and economic sovereignty, equitable distribution of the opportunities for power and wealth, and a self-reliant economy effectively controlled by Filipinos, do ordain and promulgate this Constitution and By-Laws.

We want that the people take part in the formation of the laws, and in the distribution and investment of the contributions.

We place conjugate prior distributions on the unknown mean and variance, i. e. the mean also follows a Gaussian distribution while the precision follows a gamma distribution.