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But keep in mind this formula is only an approximation, just as the relationship between the birthday problem and the birth mate problem is approximate. ... Note that the formula obtained in the binomial approximation to the birthday problem, while an approximation of the birthday probability, is basically the same as the exact birthmate probability formula ...doi:10.1080/10724117.2001.12021829 fatcat:ndk7hbnvbrfudohoenuz6pklcq
This article provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with the matching and the birthday problems. ... A large number of examples, many not well known, are provided to help a reader have a feeling for these questions at an intuitive level. ... Acknowledgements It is a pleasure to thank Jim Pitman and Shelley Zacks for their help and comments. References Abramson, M., Moser, W., 1970. More birthday surprises. Amer. Math. ...doi:10.1016/j.jspi.2003.11.015 fatcat:b7bri4btgjgvllh2xtw4lib4hm
Extensive treatment of the birthday problem is found, for instance, in [2, pp. 31, 46, 210] . ... Since (13) holds for all n ~ N, we may match the coefficients of like powers of n to obtain equation (11). In the sequel for_nwls, (10) is a simple consequence of (12),(3)and(5). ...doi:10.1016/0898-1221(91)90203-g fatcat:fzkzcgnoqjglpizv2eftfwth4y
We show that Bernoulli numbers can be used to derive arbitrarily exact bounds on the probability of a birthday surprise. ... A birthday surprise is the event that, given k uniformly random samples from a sample space of size n, at least two of them are identical. ... The term birthday surprise for a collision of (at least) two elements in the sample comes from the case n = 365, where the problem can be stated as follows: Assuming that the birthday of people distributes ...doi:10.1016/s0166-218x(02)00396-7 fatcat:lbz4z5bhmrf6lmypm7wkpqx6d4
This is the simple and hugely famous question, how many people do you need in a room for the probability to be at least 0.5 that some pair of them will have the same birthday? ... One lesson that has a safe place in the teaching calendar for me is the Birthday Problem, tackled fairly early on in the study of probability. ...doi:10.1111/j.1467-9639.1999.tb00817.x fatcat:hsrc5gvulzbcbbidlg2nf5z2ai
More birthday problems For many investigations of birthday coincidences, the simple model, which assumes that all N dates are equally likely, will be adequate. ... Nunnikhoven 2 examined how well the simple model approximates reality. ...doi:10.1111/j.1740-9713.2007.00246.x fatcat:vkrmtxhf4bfkzmmgf4eqpkwnva
In others a seemingly simple statement of the problem conceals serious difficulties in the path of solving it. A good example of the first type is the so-called birthday problem. ... A simple extension of the same type of argu- 499,924, 907/1,013,032,125 = 4935 approximately. ...doi:10.1080/00031305.1955.10501126 fatcat:5kuywhigkbey5m46xfmhnmksiq
B. 10165 On the approximate solution of singular integral equa- tions. (Russian) Problems of applied mathematics—Musheliavili eightieth birthday collection. Sakharth. SSR Mecn. Akad. Gamothvl. Centr. ... The problem is reduced to an initial value problem for the resolvent kernel and an auxiliary function, both of which are useful in the study of certain radiation problems. P. ...
The algebraic manipulations can be programmed on a computer, for instance, by representing the CF's using cubical complexes ,  extended for multiple values of the constituent variables. ... The technique described here can be used for formal verification, since it transforms a network into a series of logic functions. ... By a chip "failure" we mean any approximation, to a reasonably simple formula for R s y s ( f ) and k r MTTF. ...doi:10.1109/12.75143 fatcat:6ijfmoidzzdq5ipzrxmoiju63e
The algebraic manipulations can be programmed on a computer, for instance, by representing the CF's using cubical complexes ,  extended for multiple values of the constituent variables. ... The technique described here can be used for formal verification, since it transforms a network into a series of logic functions. ... By a chip "failure" we mean any approximation, to a reasonably simple formula for R s y s ( f ) and k r MTTF. ...doi:10.1109/tc.1978.1674968 fatcat:ed43gopxfva5fb2h2ko6srrdau
Composition schemes are then particularly helpful to obtain higher-order meth- ods while retaining the properties of simple lower-order updating formulas. ... Normally, construct- ing low order numerical formulas that preserve the structure is often much easier than going directly for higher-order formulas that preserve the structure. ...
This is a problem of best approximation in the space H’ by elements of a (nonlinear) manifold. ... Aliev, Rafik M. 10968 The convergence of a general cubature formula for certain classes of functions, and an extremal problem. (Russian) Functional analysis and its application (Russian), pp. 14-21. ...
The approximate formula developed by Bowker was found to be good only for large samples. An approximate formula is developed here which can be used for both small and large samples.” ... Authors’ summary: “The well-known birthday problem asks for the probability of at least one match out of a group of n people. ...
Various numerical methods have therefore been proposed to solve such problems. In the present paper, a method of approximation is proposed. ... Continuum mechanics and related problems of analysis (on the occasion of the eightieth birthday of Academician N. I. Musheli§- vili) (Russian), pp. 597-604. Izdat. “Nauka”, Moscow, 1972. ...
In the first part the author describes how to construct rational basis functions in order to solve the approximation problem “for a continuous function whose values are specified on the threads of a convex ... The author is concerned with this problem in the case in which the differentiation formula is derived from the n-point Lagrangian interpolation polynomial. ...
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