For the Smith-Hughes, George-Barden, and National Defense Act of 1958, the cumulative total of Federal expenditures in 42 years was only about $740 million.

For every real number x, the cumulative distribution function of a real-valued random variable X is given by

For a probability density function f ( x ) with the cumulative distribution function F ( x ), the Lorenz curve L ( F ( x )) is given by:

For a population of discrete values, or for a continuous population density, the th-quantile is the data value where the cumulative distribution function crosses.

For n independent and identically distributed continuous random variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > with cumulative distribution function G ( x ) and probability density function g ( x ) the range of the X < sub > i </ sub > is the range of a sample of size n from a population with distribution function G ( x ).

For n nonidentically distributed independent continuous random variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > with cumulative distribution functions G < sub > 1 </ sub >( x ), G < sub > 2 </ sub >( x ), ..., G < sub > n </ sub >( x ) and probability density functions g < sub > 1 </ sub >( x ), g < sub > 2 </ sub >( x ), ..., g < sub > n </ sub >( x ), the range has cumulative distribution function

For n independent and identically distributed discrete random variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > with cumulative distribution function G ( x ) and probability mass function g ( x ) the range of the X < sub > i </ sub > is the range of a sample of size n from a population with distribution function G ( x ).

For example, one may say that " there's apple in this sauce ," and then apple has cumulative reference, and, hence, is used as a mass noun.

For example, the inverse of cumulative Gaussian distribution

For example, the sequence of cumulative sums of a sequence with ordinary generating function G ( a < sub > n </ sub >; x ) has the generating function because 1 /( 1-x ) is the ordinary generating function for the sequence ( 1, 1, ...).

For a bar of material with cross-sectional area A that is wetted on one end, the cumulative volume V of absorbed liquid after a time t is

For example, an individual with a mutation in BRCA1 has a 65 % cumulative risk of breast cancer.

For his cumulative work, he was awarded the Prix Poncelet in 1898.

For example, to compute the total costs of units 1 to 200, an analyst could compute the cumulative average cost of unit 200 and multiply this value by 200.

For the most part, cumulative records are no longer graphed using rotating drums, but are recorded electronically instead.

For undergraduates, as of 2004, the school has started an honor's program that allows for the awarding of an honor's degree upon graduation, if certain honor's course requirements and academic standards ( ex: maintaining a cumulative 3. 0 ) have been maintained.

For children and adolescents who use indoor tanning facilities for cosmetic reasons, the focus on perceived, immediate benefits overshadows the cumulative risks and consequences in the future.

For the 11 years ending in December 1999, Medallion ’ s cumulative returns were 2, 478. 6 percent.

For subsequent rounds, players are sorted according to their cumulative scores and players are assigned opponents that have the same or similar score to that point.

For a uniform distribution of radio sources the slope of the cumulative distribution of log ( number, N ) versus log ( power, S ) would have been-1. 5, but the Cambridge data apparently implied a ( log ( N ), log ( S )) slope of nearly-3. 0.

For a uniform distribution of radio sources at not too large redshift ( i. e. in a ' steady-state, Euclidean universe ') the slope of the cumulative distribution of log ( N ) versus log ( S ) would be − 1. 5.

For instance, CMF-therapy for breast cancer ( where the cumulative dose is typically less than 20 grams of cyclophosphamide ) seems to carry an AML risk of less than 1 / 2000th, with some studies even finding no increased risk compared to the background population.

For comparison, the cumulative total of AIDS cases in the USA through 1997 is 641, 087.

* For a normal distribution, the arithmetic mean is equal to both the median and the mode, other measures of central tendency.

For example, as in pin and as in spin are allophones for the phoneme in the English language because they cannot distinguish words ( in fact, they occur in complementary distribution ).

For most players, many calls ( bids, doubles and redoubles, and sometimes even passes ) are not made with the intention that they become the final contract, but to describe the strength and distribution of the player's hand, so that the partnership can reach an informed conclusion on their best contract, and / or to obstruct the opponents ' bidding.

For example, the traditional common law rule through most of the 19th century was that a plaintiff could not recover for a defendant's negligent production or distribution of a harmful instrumentality unless the two were in privity of contract.

For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.

For example, if n samples are taken from a Cauchy distribution, one may calculate the sample mean as:

For certain types of point sets, such as a uniform random distribution, by intelligently picking the splitting lines the expected time can be reduced to O ( n log log n ) while still maintaining worst-case performance.

For example, J. B. Clark saw the co-ordinating function in production and distribution as being served by entrepreneurs ; Frank Knight introduced managers who co-ordinate using their own money ( financial capital ) and the financial capital of others.

For example, the illegal manufacture, distribution or possession of controlled substances may be a felony, although possession of small amounts may be only a misdemeanor.

For the next two years, Hoover worked 14-hour days from London, administering the distribution of over two million tons of food to nine million war victims.

For most types of hashing functions the choice of the function depends strongly on the nature of the input data, and their probability distribution in the intended application.

For instance, if we impose some requirements on a distribution f, we can attempt to translate these requirements in terms of the Fourier transform of f. The Paley – Wiener theorem is an example of this.

For a symmetric distribution ( where the median equals the midhinge, the average of the first and third quartiles ), half the IQR equals the median absolute deviation ( MAD ).

For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site ( including a quip about the mass of Eötvös himself ), see Franklin.

For easier distribution of large programs, multiple class files may be packaged together in a. jar file ( short for Java archive ).

For a continuous charge distribution in motion, the Lorentz force equation becomes:

For some people, the obvious solution to this concern is to redefine the wage structure politically to achieve a socially preferable distribution of income.

For a probability distribution, the mean is equal to the sum or integral over every possible value weighted by the probability of that value.

For example, mainline churches, with their upper class congregations, " promote order, stability, and conservatism, and in so doing proved to be a powerful source of legitimation of the status quo and of existing disparities in the distribution of wealth and power " because much of the wealth of the church comes from the congregation.

For example, the Internet includes web sites, blogs, podcasts, and various other technologies built on top of the general distribution network.

For example, this map of Europe has been distorted to show population distribution, while the rough shape of the continent is still discernable.

For the special case where is a joint probability distribution and the loss function is the negative log likelihood a risk minimization algorithm is said to perform generative training, because can be regarded as a generative model that explains how the data were generated.