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We can differentiate distributions by defining their derivatives via differentiated test functions.
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We and can
We have staved off a war and, since our behavior has involved all these elements, we can only keep adding to our ritual without daring to abandon any part of it, since we have not the slightest notion which parts are effective.
We assume for this illustration that the size of the land plots is so great that the distance between dwellings is greater than the voice can carry and that most of the communication is between nearest neighbors only, as shown in Figure 2.
We hear equally fervent concern over the belief that we have not enough generalists who can see the over-all picture and combine our national skills and knowledge for useful purposes.
We can also argue that the three brothers Karamazov and Smerdyakov were the external representatives of an internal conflict within one man, Dostoevsky, a conflict having to do with father-murder and the wish to possess the father's woman.
We feel uncomfortable at being bossed by a corporation or a union or a television set, but until we have some knowledge about these phenomena and what they are doing to us, we can hardly learn to control them.
We must avoid the notion, suggested to some people by examples such as those just mentioned, that ideas are `` units '' in some way comparable to coins or counters that can be passed intact from one group of people to another or even, for that matter, from one individual to another.
We can be virtuous only if we control our lower natures, the passions in this case, and strengthen our rational side ; ;
We can force Britain and France out of the Suez, but we cannot so much as try to force the Russian tanks back from Budapest.
We can vote in the UN against South African apartheid or Portuguese rule in Angola, but we cannot even introduce a motion on the Berlin Wall -- much less, give the simple order to push the Wall down.
We can no longer rely on interdepartmental machinery `` somewhere upstairs '' to resolve differences between this and other departments.
We have developed an ingenious method of interlocking these so that you can make the major part of your house in your own workshop, panel by panel, according to plan.
We gently usher them to an island of tables and chairs strategically placed on the far side of the pool where they can amuse each other until we get ready to merge sides.
We found that three men -- two carpenters and a helper -- can put up wall panels or trusses more economically than four men -- because four men don't make two teams ; ;
We and differentiate
We can also differentiate both sides of the integral equation with respect to s to obtain the local, or instantaneous, form of the law:
We use the term Celtic Traditionalist to differentiate us from the ones who claim to be Welsh, and I know of only one tradition that has the right to use that name.
:* The Covenantal Principle: " We differentiate between the various contracts that God has made with his people ; specifically their provisions, their parties and their purposes.
W. J. T. Mitchell trenchantly observed that " We tend to think that to compare poetry with painting is to make a metaphor, while to differentiate poetry from painting is to state a literal truth.
We took the concept, and said, " What can we do to differentiate this to make this different from the Dynasty Warriors games?
We and distributions
We use Lagrange multipliers to find the point of maximum entropy,, across all discrete probability distributions on.
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 denote the canonical probability distributions for the Hamiltonian and the trial Hamiltonian by and, respectively.
We denote the diagonal components of the density matrices for the canonical distributions for and in this basis as:
We use cumulative distribution functions ( cdf ) in order to encompass both discrete and continuous distributions.
* We speak of perfect zero-knowledge if the distributions produced by the simulator and the proof protocol are distributed exactly the same.
* We speak of computational zero-knowledge if no efficient algorithm can distinguish the two distributions.
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.
We can expand the expectations, using the standard formulas for the expectations of moments of the Gaussian and gamma distributions:
We then have values for the hyperparameters of the approximating distributions of the posterior parameters, which we can use to compute any properties we want of the posterior — e. g. its mean and variance, a 95 % highest-density region ( the smallest interval that includes 95 % of the total probability ), etc.
We did not assume this ; the only assumption we made was that the distributions factorize, and the form of the distributions followed naturally.
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