Translation and analysis of words by ChatGPT artificial intelligence
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random graph hypothesis - translation to English
Ex: Results indicate that consistent numbers of components are produced under the random graph hypothesis across various applications.
![In the [[Monty Hall problem]], when the host reveals one door that contains a goat, this provides new information that needs to be factored into the calculation of probabilities.](https://commons.wikimedia.org/wiki/Special:FilePath/Monty open door.svg?width=200 "In the [[Monty Hall problem]], when the host reveals one door that contains a goat, this provides new information that needs to be factored into the calculation of probabilities.")
![Ancient [[fresco]] of dice players in [[Pompei]]](https://commons.wikimedia.org/wiki/Special:FilePath/Pompeii - Osteria della Via di Mercurio - Dice Players.jpg?width=200 "Ancient [[fresco]] of dice players in [[Pompei]]")
![pseudorandomly generated]] [[bitmap]].](https://commons.wikimedia.org/wiki/Special:FilePath/RandomBitmap.png?width=200 "pseudorandomly generated]] [[bitmap]].")
![The ball in a [[roulette]] can be used as a source of apparent randomness, because its behavior is very sensitive to the initial conditions.](https://commons.wikimedia.org/wiki/Special:FilePath/Roulette wheel.jpg?width=200 "The ball in a [[roulette]] can be used as a source of apparent randomness, because its behavior is very sensitive to the initial conditions.")
Ex: Where the subcategory is small the subsequent arrangement is random.
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* at random = de un modo aleatorio, al azar
* fuzzy random variable = variable aleatoria de lógica difusa
* pick at + random = escoger al azar, escoger aleatoriamente
* random access = acceso aleatorio
* random access file = fichero de acceso aleatorio
* random access memory (RAM) = memoria de acceso aleatorio (RAM)
* random act of = acto espontáneo de
* random clumping = plantación irregular
* random facts = hechos dispersos
* random fuzzy set = conjunto aleatorio de lógica difusa
* random graph hypothesis = ?
* random sample = muestra probablística, muestra al azar
* random sampling = muestreo probabilístico, muestreo al azar
* simple random sampling = muestreo probabilístico simple, muestreo al azar simple
* stratified random sampling = muestreo probabilístico estratificado, muestreo al azar estratificado
![If the sample space is the set of possible numbers rolled on two dice, and the random variable of interest is the sum ''S'' of the numbers on the two dice, then ''S'' is a discrete random variable whose distribution is described by the [[probability mass function]] plotted as the height of picture columns here.](https://commons.wikimedia.org/wiki/Special:FilePath/Dice Distribution (bar).svg?width=200 "If the sample space is the set of possible numbers rolled on two dice, and the random variable of interest is the sum ''S'' of the numbers on the two dice, then ''S'' is a discrete random variable whose distribution is described by the [[probability mass function]] plotted as the height of picture columns here.")
Definition
Wikipedia
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at random for each pair of its vertices whether to connect the vertices by an edge. The names of this graph honor Richard Rado, Paul Erdős, and Alfréd Rényi, mathematicians who studied it in the early 1960s; it appears even earlier in the work of Wilhelm Ackermann (1937). The Rado graph can also be constructed non-randomly, by symmetrizing the membership relation of the hereditarily finite sets, by applying the BIT predicate to the binary representations of the natural numbers, or as an infinite Paley graph that has edges connecting pairs of prime numbers congruent to 1 mod 4 that are quadratic residues modulo each other.
Every finite or countably infinite graph is an induced subgraph of the Rado graph, and can be found as an induced subgraph by a greedy algorithm that builds up the subgraph one vertex at a time. The Rado graph is uniquely defined, among countable graphs, by an extension property that guarantees the correctness of this algorithm: no matter which vertices have already been chosen to form part of the induced subgraph, and no matter what pattern of adjacencies is needed to extend the subgraph by one more vertex, there will always exist another vertex with that pattern of adjacencies that the greedy algorithm can choose.
The Rado graph is highly symmetric: any isomorphism of its finite induced subgraphs can be extended to a symmetry of the whole graph. The first-order logic sentences that are true of the Rado graph are also true of almost all random finite graphs, and the sentences that are false for the Rado graph are also false for almost all finite graphs. In model theory, the Rado graph is an example of the unique countable model of an ω-categorical theory.
