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In the mathematical theory of probability, the '''Heyde theorem'''&nbsp;is the [[characterization (mathematics)|chara ...<math>\xi_j, j = 1, 2, \ldots, n, n \ge 2</math>&nbsp; be [[independence (probability theory)|independent]] random variables. Let <math>\alpha_j, \beta_j</math>& ...

...alently the limiting behavior of distribution’s [[Characteristic function (probability theory)|characteristic function]]. ...4/aos/1176348248|doi-access=free}}</ref> if its [[Characteristic function (probability theory)|characteristic function]] satisfies ...

* A has a higher probability than B of receiving the best outcome. ...ave an equal probability of receiving the best outcome, but A has a higher probability of receiving the 2nd-best outcome. ...

...goes to 1 as ''n'' goes to infinity, i.e. the probability of the [[Event (probability theory)|event]] occurring can be made as close to 1 as desired by making '' ...en when the number of nodes is very large, the algorithm is correct with a probability that is very near 1. This fact is expressed shortly by saying that the algo ...

...nce|inverse problems]] on [[function space]]s for which a Gaussian [[prior probability|Bayesian prior]] is an inappropriate model. The construction of a Besov me ...\xi_{n} |^{p} )</math>. Informally, <math>u</math> can be said to have a probability density function proportional to <math>\exp (- \tfrac{\kappa}{2} \| u \|_{X ...

===Problems with Metropolis–Hastings=== ...ses, one uses a Gaussian distribution centered on the current point in the probability space, of the form <math>Q(x'; x^t)=\mathcal{N}(x^t;\sigma^2 I) \,</math>. ...

...of a probability distribution''' accordingly states that it is the only [[probability distribution]] that satisfies specified conditions. More precisely, the mod ...>. By characterizations of probability distributions we understand general problems of description of some set <math> \mathcal{C}</math> in the space <math> \m ...

{{Short description|Theorem in probability theory}} ...rnal|last=Rukhin A. L.|date=1970|title=Certain statistical and probability problems on groups|journal=Trudy Mat. Inst. Steklov|volume=111|pages=52–109}}</ref>< ...

{{Short description|Probability problem}} The '''Newton–Pepys problem''' is a [[probability]] problem concerning the probability of throwing sixes from a certain number of dice.<ref name="wolfram">{{MathW ...

...entary event|complement]] of failure <math>(\text{Reliability} = 1 - \text{Probability of Failure})</math>. The failure occurs when the total applied load is larg ...and resistances are explicit and have their own independent function, the probability of failure could be formulated as follows.<ref name=":0" /><ref name=":1" / ...

...processes where certain constraints need to be satisfied with a specified probability. ...[probability]] and confidence levels to handle uncertainty in optimization problems. It distinguishes between single and joint chance constraints: ...

...simpler subsets. In [[probability theory]] it is the approximation of one probability distribution by another. ...and not&nbsp;''P''. One straightforward way to compute an ε-net with high probability is to take a sufficient number of random points, where the number of random ...

==Related problems== Similar problems describe the [[bipartite graph|degree sequence]]s of [[bipartite graph|simp ...

In [[probability theory]] and [[statistics]], the '''generalized multivariate log-gamma (G-M ==Joint probability density function== ...

...tant. It is a [[randomized algorithm]] whose running time is O(''n'') with probability close to 1. The protocol was developed by [[Jeff Edmonds]] and [[Kirk Pruhs The algorithm guarantees that, with high probability, each partner receives at least half of one of his candidate pieces, which ...

...m that succeeds with high probability (having a polynomially small failure probability).{{r|yv}} If so, this would be optimal, as connected components can be cons ...l complexity class [[NC (complexity)|NC¹]] does not contain all problems in [[polynomial time]], which would be a significant advance on current kno ...

{{Short description|Continuous probability distribution}} {{Probability distribution | ...

...n percolation |url=https://www.jstor.org/stable/2652916 |journal=Annals of Probability |volume=29 |issue=1 |pages=123–126 |doi=10.1214/aop/1008956324 |jstor=26529 ...upper bunk and their corresponding edges in the lower bunk share the same probability. The probabilities assigned to the posts can be arbitrary. ...

...machine in polynomial time, upon measuring the first qubit, with an error probability of at most 1/poly(n) for all instances.<ref name="shorjordan2008" /> ...ty)|BPP]], [[BQP]], and [[RP (complexity)|RP]] are agnostic to the precise probability gap, because any polynomial acceptance gap can be ''amplified'' to a fixed ...

...le:Warehouse md17.jpg|thumb|Regenerative processes have been used to model problems in inventory control. The inventory in a warehouse such as this one decreas ...tions | doi = 10.1016/B978-0-12-375686-2.00003-0 | title = Introduction to Probability Models | pages = 421–641 | year = 2010 | isbn = 9780123756862 }}</ref> This ...