Using Bayesian reasoning, a simple theory is preferred to a complicated one because of a higher prior probability.

Using Carnap's formula for induction, he finds that the probability that all ravens are black decreases from 0. 9985 to 0. 8995 when it is discovered that one of the two objects is a black raven.

Using a random number c from a uniform distribution as the probability density to " pass by ", we get

Using this form we can use trigonometric identities to compute the probability of observing ω after r iterations mentioned in the previous section,

Using the Coupon collector's problem in probability theory, it can be shown that it takes, on average, 72 questions of the Magic 8 Ball for all 20 of its answers to appear at least once.

Using the equation above, the probability of exactly two tosses out of four total tosses resulting in a heads is given by:

Using the raw count and this probability function, one can arrive at an estimate of the actual density of objects.

Using this formula, Craig derived that the probability of the story of Jesus would reach 0 in the year 3150.

Using the chi-squared distribution to interpret Pearson's chi-squared statistic requires one to assume that the discrete probability of observed binomial frequencies in the table can be approximated by the continuous chi-squared distribution.

Using this procedure each element in the population has a known and equal probability of selection.

Using this notation and some knowledge about mathematical functions and probability theory we formalise different versions of the binding and hiding properties of commitments.

Using the infinitesimal notation, the polar form form of the probability above is simply

Using AIC, instead of AICc, when n is not many times larger than k < sup > 2 </ sup >, increases the probability of selecting models that have too many parameters, i. e. of overfitting.

Using the Dirac adjoint, the conserved probability four-current density for a spin-1 / 2 particle field

Using the media to change perceptions of ethnicity might lead to a change in probability of ethnic violence.

Using the standard formalism of probability, let and be two random variables defined on probability spaces and.

* Familiarity: Using common, well-known code, software, operating systems, and / or hardware increases the probability an attacker has or can find the knowledge and tools to exploit the flaw

Using 3d6 for checks subjects it to the more predictable " bell curve " and has a higher probability of success.

Using pulse compression also reduces the probability of detection, since the peak transmitted power is lower while the range and resolution is the same.

# Using them increases the probability of compatibility between objects designed at different times by different people.

Using Bayes ' theorem, the posterior probability density of r conditional on h and t is expressed as follows:

Using a URI ( such as < nowiki >" http :// www. w3. org / 1999 / xhtml "</ nowiki >) to identify a namespace, rather than a simple string ( such as " xhtml "), reduces the probability of different namespaces using duplicate identifiers.

Using this approximation, it can be shown that around 95 % of this distribution's probability lies within 2 standard deviations of the mean.

Using a branch of mathematics known as tuple calculus, he demonstrated that such a system could support all the operations of normal databases ( inserting, updating etc.

Using these two examples, we can make some useful observations that motivate the major ideas in lambda calculus.

Using the techniques of differential calculus, the velocity and acceleration as a function of time can be found:

Using differential calculus, we can determine the limit, or the value that Δy / Δx approaches as Δy and Δx get closer to zero ; it follows that this limit is the exact slope of the tangent.

Using geometry and calculus, some simple combinations of sources are easily solved ; others are not.

Using a method called " calculus of statement ," Lentz helps the team to mitigate the pressure harming the plant operators.

Using the fundamental theorem of calculus often requires finding an antiderivative.

Using this in the sum, one can evaluate the remaining integral using the calculus of residues and arrive at the desired generating function.

Using the limit notation of calculus, the volume may be expressed as:

Using tensor calculus, proper time is more rigorously defined in general relativity as follows: Given a spacetime which is a pseudo-Riemannian manifold mapped with a coordinate system and equipped with a corresponding metric tensor, the proper time experienced in moving between two events along a timelike path P is given by the line integral

Using differential calculus we can obtain conditions on x under which this holds.

Using the parametrization of the hyperbola with hyperbolic angle, the theory of special relativity provided a calculus of relative motion with the one-parameter group indexed by rapidity.

* Using process calculus to model biological systems ( stochastic-calculus, BioAmbients, Beta Binders, BioPEPA, Brane calculus ).

Using calculus, Gershun could compute the irradiance falling on points () on a surface.

Using the functional calculus for larger classes of functions, we can for example define rigorously the " square root " of the ( negative ) Laplacian operator − Δ or the exponential

Using the bounded functional calculus, one can prove part of the Stone's theorem on one-parameter unitary groups:

Using typed lambda calculus to implement formal systems on a machine.

Using modern predicate calculus, we quickly discover that the statement is ambiguous.