For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object.

For normal calculation a number zero is often needed, here most notably when calculating the number of years in a period that spans the epoch ; the end years need only be subtracted from each other.

For international banks, including the 55 member central banks of the Bank for International Settlements, the threshold is 8 % ( see the Basel Capital Accords ) of risk-adjusted assets, whereby certain assets ( such as government bonds ) are considered to have lower risk and are either partially or fully excluded from total assets for the purposes of calculating capital adequacy.

For stationary and shaft engines including propeller engines, fuel consumption is measured by calculating the brake specific fuel consumption, which measures the mass flow rate of fuel consumption divided by the power produced.

These specifications were provided by calculating adequate intakes from measured intakes in populations of individuals with “ desirable osmolarity values of urine and desirable water volumes per energy unit consumed .” For healthful hydration, the current EFSA guidelines recommend total water intakes of 2. 0 L / day for adult females and 2. 5 L / day for adult males.

For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times.

For many rough uses ( for instance, calculating an approximate phase of the Moon ), this position, as seen from the Earth's center, is adequate.

For applications requiring precision ( for instance, calculating the shadow path of an eclipse ), the Almanac gives formulae and methods for calculating the topocentric coordinates, that is, as seen from a particular place on the Earth's surface, based on the geocentric position.

For example, there is little problem in calculating the weight of the snow, which provides information about the load on a weak layer.

For instance, if one measured the distance along a straight line or spacelike geodesic between the two points, observers situated between the two points would have different cosmological ages when the geodesic path crossed their own world lines, so in calculating the distance along this geodesic one would not be correctly measuring comoving distance or cosmological proper distance.

For the purposes of calculating the amount of income subject to garnishments, United States ' federal law defines disposable income as an individual's compensation ( including salary, overtime, bonuses, commission, and paid leave ) after the deduction of health insurance premiums and any amounts required to be deducted by law.

For example in wireless communications the channel can be modelled by calculating the reflection off every object in the environment.

For many mechanical data processing machines, such as the IBM punched card accounting machines, their calculating operations were directed by the use of a quick-swap control panel wired to route signals between module sockets.

For example, if one is calculating the average temperature of 10 objects in a room, and nine of them are between 20 and 25 degrees Celsius, but an oven is at 175 ° C, the median of the data could be between 20 and 25 ° C but the mean temperature will be between 35. 5 and 40 ° C.

For example, under the Basel II agreement of the Basel Committee on Banking Supervision, banking regulators can allow banks to use credit ratings from certain approved CRAs ( called " ECAIs ", or " External Credit Assessment Institutions ") when calculating their net capital reserve requirements.

For rockets the ' absence of external forces ' usually is taken to mean the absence of atmospheric drag as well as the absence of aerostatic back pressure on the nozzle and hence the vacuum Isp is used for calculating the vehicle's delta-v capacity via the rocket equation, and the costs for the atmospheric losses are rolled into the delta-v budget when dealing with launches from a planetary surface.

For example, it is possible to find shortest paths and longest paths from a given starting vertex in DAGs in linear time by processing the vertices in a topological order, and calculating the path length for each vertex to be the minimum or maximum length obtained via any of its incoming edges.

For purposes of calculating income, this should be treated the same way as if Y gave X $ 50, 000.

For example in India about 435 items were used for calculating the WPI in base year 1993-94 while the advanced base year 2004-05 uses 676 items.

For homogeneous isotropic materials simple relations exist between elastic constants ( Young's modulus E, shear modulus G, bulk modulus K, and Poisson's ratio ν ) that allow calculating them all as long as two are known:

For example, twistor string theory may simplify calculating scattering amplitudes from Feynman diagrams.

For more complex survey designs, different formulas for calculating the standard error of difference must be used.

For example, Fomenko compares the contemporary history of Rome written by Titus Livius with a modern history of Rome written by Russian historian V. S. Sergeev, calculating that the two have high correlation, and thus that they describe the same period of history, which is undisputed.

For example, if you were to truncate a sample with 8 entries by 12. 5 %, you would discard the first and the last entry in the sample when calculating the truncated mean.

For an experiment to qualify as a binomial experiment, it must have four properties: ( 1 ) there must be a fixed number of trials, ( 2 ) each trial must result in a `` success '' or a `` failure '' ( a binomial trial ), ( 3 ) all trials must have identical probabilities of success, ( 4 ) the trials must be independent of each other.

For subjectivists rationality and coherence constrain the probabilities a subject may have, but allow for substantial variation within those constraints.

For a discrete probability function f ( y ), let y < sub > i </ sub >, i = 1 to n, be the points with non-zero probabilities indexed in increasing order ( y < sub > i </ sub > < y < sub > i + 1 </ sub >).

For example, one can talk about motion of a wave or a quantum particle ( or any other field ) where the configuration consists of probabilities of occupying specific positions.

For small bit error probabilities, this is approximately

For example, if two events are Heads and Tails, then the probability of Heads-or-Tails must be equal to the sum of probabilities for Heads and Tails ).

For example, given three elements 1, 2 and 3 with probabilities 1 / 4, 1 / 4 and 1 / 2, the value assigned to

For sufficiently nice prior probabilities, the Bernstein-von Mises theorem gives that in the limit of infinite trials and the posterior converges to a Gaussian distribution independent of the initial prior under some conditions firstly outlined and rigorously proven by Joseph Leo Doob in 1948, namely if the random variable in consideration has a finite probability space.

For example, the transition probabilities from 5 to 4 and 5 to 6 are both 0. 5, and all other transition probabilities from 5 are 0.

For example, the probability of flipping two coins ( coin A and coin B ) and having at least one land head-up can be expressed as the sum of the probabilities for three specific events: coin A heads (↑) with B tails (↓), coin A heads (↑) with B heads (↑), and coin A tails (↓) with B heads (↑).

For a particle described by probability theory random walking on a line, the analogous thing is the list of probabilities, which give the probability of any position.

For this to be a probability distribution the sum of the probabilities at each point must equal 1, so our constraint is

For example if the constant, c, equals 1, the probabilities of a move to the left at positions x

For example, if these models are not grounded in Hilbert spaces and probabilities, they belong to the class of theories with local hidden variables that some deem ruled out experimentally using Bell's theorem.

For example, geometry has its origins in the calculation of distances and areas in the real world ; statistics has its origins in the calculation of probabilities in gambling ; and algebra started with methods of solving problems in arithmetic.

For all words in each training email, the filter will adjust the probabilities that each word will appear in spam or legitimate email in its database.

For example, assuming the individual probabilities follow a chi-squared distribution with 2N degrees of freedom, one could use the formula:

For other channel models, the messages passed between the variable nodes and check nodes are real numbers, which express probabilities and likelihoods of belief.

For instance, he claimed that the theory of probabilities was just another way of complexifying reality through a deepening of rationality ( even though critics like Lord Kelvin found this theory irrational ).

For such ratio distributions, there can be defined probabilities for intervals which can be defined either by Monte Carlo simulation, or, in some cases, by using the Geary-Hinkley transformation.

For toy Feistel ciphers, it was observed that those with complex and well-designed key schedules can reach a uniform distribution for the probabilities of differentials and linear hulls faster than those with poorly-designed key schedules.

For example, in case of medical emergency, there may not be enough time to do any detailed calculations or estimations of different probabilities, in which case the ABC protocol may be more appropriate.

For example, suppose we wish to test whether a coin is fair ( i. e. has equal probabilities of producing a head or a tail ).