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	Random sequence - Wikipedia, the free encyclopedia
		In short, a random sequence is a sequence of random variables.
		Also, the statement of the central limit theorem (essentially that the average of a number of observations converges to the mean value) involves an infinite sequence of independent identically-distributed random variables.
		The term "random sequence" can also describe a sequence of random numbers : Algorithmic information theory defines a random sequence as one that is shorter than any computer program that can produce that sequence (Chaitin-Kolmogorov randomness).
	en.wikipedia.org /wiki/Random_sequence (183 words)

	Random sequence -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		A random sequence is a kind of (A statistical process involving a number of random variables depending on a variable parameter (which is usually time)) stochastic process.
		In short, a (Click link for more info and facts about random) random sequence is a (Serial arrangement in which things follow in logical order or a recurrent pattern) sequence of (A variable quantity that is random) random variables.
		Random sequences are essential in (A branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters) statistics.
	www.absoluteastronomy.com /encyclopedia/r/ra/random_sequence.htm (332 words)

	Pseudorandom number generator - Wikipedia, the free encyclopedia
		While "truly" random numbers can be generated using hardware random number generators, pseudorandom numbers are a critical part of modern computing, from cryptography to the Monte Carlo method for simulating physical systems.
		Most cryptography relies on the assumption that it is infeasible to distinguish a suitable PRNG from noise; the simplest example is a stream cipher, which (often) works by taking the exclusive or of the secret message with the output of a PRNG.
		The RANDU random number algorithm used for decades on mainframe computers was flawed, and much research work of that time is less reliable than it should have been as a result.
	en.wikipedia.org /wiki/Pseudorandom_number_generator (1143 words)

	Cryptographically secure pseudo-random number generator - Wikipedia, the free encyclopedia
		Ideally, the generation of these random numbers uses entropy obtained from another source, which might be a hardware random number generator or perhaps unpredictable system processes — though unexpected correlations have been found in several such ostensible processes.
		From an information theoretic point of view the amount of randomness, the entropy, that can be generated is equal to the entropy that went in to the system.
		CSPRNG requirements fall into two groups: first that their statistical properties are good (passing tests of randomness), second that they hold up well in case of attack, even when (part of) their secrets are revealed.
	en.wikipedia.org /wiki/Cryptographically_secure_pseudo-random_number_generator (902 words)

	Random Sequence Generation by Cellular Automata (1986)
		The degree of randomness of a sequence can be defined in terms of the classes of computations which cannot discern patterns in it.
		A sequence is ``random enough'' for application in a particular system if the computations that the system effectively performs are not sophisticated enough to be able to find patterns in the sequence.
		Random sequence generators have been constructed with the property that recognizing patterns in the sequences they produce is in principle equivalent to solving certain difficult number theoretical problems [2] (which are in the class NP, but are not NP-complete).
	www.stephenwolfram.com /publications/articles/computation/86-random/2/text.html (1058 words)

	Updates
		As odd as this may sound, the generation of random numbers is something of a science with a long history and lots of theory.
		If a sequence of random numbers may be generated only by a program that is as long as the sequence itself, then the sequence is random.
		Random numbers may be divided into two categories: semi-random numbers (called pseudo-random numbers) and genuinely random numbers.
	www.glencoe.com /norton/n-instructor-/updates/2000/21100.html (1361 words)

	Science News Online (6/12/99): Fibonacci at Random
		He found that the hundredth term in such a sequence, for example, is approximately equal to the hundredth power of the number 1.13198824....
		Random Fibonacci sequences might have leveled off to a constant absolute value because of the subtractions, for example, but they actually escalate exponentially.
		In a different mathematical context involving so-called random matrix multiplication, Furstenberg and Kesten had proved that in number sequences generated by certain types of processes having an element of randomness, the value of the nth term of the sequence gets closer to the nth power of some fixed number.
	www.sciencenews.org /sn_arc99/6_12_99/bob1.htm (1142 words)

	Infinite monkey theorem - Wikipedia, the free encyclopedia
		Typing at random, the chance that the first letter typed is b is 1/50, as is the chance that the second letter typed is a, and so on.
		Given an infinite string where each character is chosen uniformly at random, any given finite string almost surely (with probability 1) occurs as a substring at some position (and indeed, infinitely many positions).
		Given an infinite sequence of such infinite strings, where each character of each string is chosen uniformly at random, any given finite string almost surely occurs as a prefix of one these infinite strings (and indeed, as a prefix of infinitely many of these strings in the sequence).
	en.wikipedia.org /wiki/Infinite_monkey_theorem (2429 words)

	>HG324 Random Bit Generator
		Random bits (numbers) produced by HG324 generator pass, with a high probability, any known standard statistical randomness test such as: Frequency test, ChiSquare, Entropy, Autocorrelation test, KS test, picturing randomness and others, as well as the most stringent ones: the Marsaglia's Diehard battery of tests, the Coron's version of Maurer's Universal Statistical Test.
		A long sequence of random bits should not be losslesly compressable by any known or unknown technique.
		That is, a long random sequence should not be descriobable by any sequence of bits shorter than the original sequence.
	random.com.hr /products/random/hg324.html (1422 words)

	Random (Java 2 Platform SE v1.4.2)
		The number of random bytes produced is equal to the length of the byte array.
		Linear congruential pseudo-random number generators such as the one implemented by this class are known to have short periods in the sequence of values of their low-order bits.
		Thus, this special case greatly increases the length of the sequence of values returned by successive calls to this method if n is a small power of two.
	java.sun.com /j2se/1.4.2/docs/api/java/util/Random.html (1130 words)

	Wired 11.08: Totally Random
		Random number sequences have been around for 4,000 years, but never have they been in such demand.
		A sequence is considered random if no patterns can be recognized in it - the longer the string, the stronger the encryption.
		Pollsters use the sequences to help select representative samples of the public; scientists to model chaotic molecular behavior; physicists to conduct simulations of nuclear detonations.
	www.wired.com /wired/archive/11.08/random.html (1011 words)

	Computer Generated Random Numbers
		Although there is nothing "random" about a completely deterministic computer generated sequence of numbers, we can analyze the sequence of numbers to see if there is any reason to doubt that the sequence could have come from a truly random stochastic process.
		For example, the sequence consisting of all ones {1,1,...,1} is as equally likely to occur as any other sequence, but this sequence tends not to reinforce our assumption that the die is fair.
		The first random number is used to pick an element from the array of random numbers, and the second random number is used to replace the number chosen.
	world.std.com /~franl/crypto/random-numbers.html (10155 words)

	A sequence of independent uniform (pseudo-) RNs
		In Section 1.4.1 we have stated that a sequence of random numbers does not have anything like a distribution.
		A sequence of independent uniform (P)RNs should be a sequence of numbers that behaves somewhat typical for a sequence of independent uniformly distributed random variables.
		Note that this argument is built on the definition of random numbers and does not account for the fact that the special model 'uniform distribution' assigns the same probability to every sequence of PRNs.
	random.mat.sbg.ac.at /~ste/dipl/node12.html (570 words)

	Pseudorandom Number Sequence Test Program
		The chi-square test is the most commonly used test for the randomness of data, and is extremely sensitive to errors in pseudorandom sequence generators.
		The chi-square distribution is calculated for the stream of bytes in the file and expressed as an absolute number and a percentage which indicates how frequently a truly random sequence would exceed the value calculated.
		We interpret the percentage as the degree to which the sequence tested is suspected of being non-random.
	www.fourmilab.ch /random (1326 words)

	Random number
		As the sequence itself had been imposed certain restrictions, the method of choosing the next random element (in the interval defined by restrictions) did not give the random sequence as a whole.
		If we arrange all possible sequences in certain order (for example, in lexicographical order) and assign each sequence its number, after choice of the random number it is possible to take the correspondent sequence for the random one.
		As the amount of sequences is quite large, the number can be a long one, composed of hundreds decimal digits, though our random data generator could give only normal numbers.
	acm.uva.es /p/v5/504.html (486 words)

	TechXclusives - That is So Random! (Site not responding. Last check: 2007-10-22)
		Instead, we can create a sequence of numbers that has all the appearances of a random sequence, except that it is not random.
		The sequence has all the correct properties for a random sequence of bits, such as equal number of 1’s and 0’s, but it is predictable forwards and backwards.
		In addition to being able to generate fast streams of true random numbers, you can also test the random number sequences for their properties at the same time they are being generated.
	www.xilinx.com /xlnx/xweb/xil_tx_display.jsp?sGlobalNavPick=&sSecondaryNavPick=&category=-1209667&iLanguageID=1&multPartNum=1&sTechX_ID=alsd_random (1093 words)

	Fast Uniform Random Number Generator
		generates a sequence of 32-bit floating-point random numbers uniformly distributed in the interval (0,1), the end points excluded.
		In order to restart the generation, the number of random numbers generated is recorded by the generator.
		The sequence is restarted either generating this many random numbers or saving and restoring a vector of 103 words.
	wwwasdoc.web.cern.ch /wwwasdoc/shortwrupsdir/v113/top.html (601 words)

	Uniform random number generator (Site not responding. Last check: 2007-10-22)
		This Random Number Generator is based on the algorithm in a FORTRAN version published by George Marsaglia and Arif Zaman, Florida State University.
		It passes ALL of the tests for random number generators and has a period of 2^144, is completely portable (gives bit identical results on all machines with at least 24-bit mantissas in the floating point representation).
		The algorithm is a combination of a Fibonacci sequence (with lags of 97 and 33, and operation "subtraction plus one, modulo one") and an "arithmetic sequence" (using subtraction).
	astronomy.swin.edu.au /~pbourke/analysis/random (295 words)

	Citations: Sparse random graphs with a given degree sequence - Luczak (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		considered the asymptotic behavior of the largest component of a random graph with given degree sequence as a function of the number of vertices of degree 2.
		In this paper, we are interested in random graphs with a fixed degree sequence where each graph with that degree sequence is chosen with equal probability.
		As [13] proves the case where r n 1=2 log n, this implies G r is r connected and Hamiltonian whp 1 for all 3 r n 4.
	citeseer.ist.psu.edu /context/1090569/0 (795 words)

	Which properties of a random sequence are dynamically sensitive?, Itai Benjamini, Olle Häggström, Yuval ...
		Consider a sequence of i.i.d.\ random variables, where each variable is refreshed (i.e., replaced by an independent variable with the same law) independently, according to a Poisson clock.
		sequence of unbiased random bits, the random set of times t where $\alpha \log_2(n)$ bits among the first n bits can be predicted from their predecessors, has Hausdorff dimension $1-\alpha$ a.s.
		Finally, we consider simple random walk in the lattice $\Z^d$, and prove that transience is dynamically stable for $d \ge 5$, and dynamically sensitive for $d=3,4$.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aop/1046294302 (656 words)

	NESC0843: RANDOM_NUMBERS, Random Number Sequence Generated from Gas Ionisation Chamber Data (Site not responding. Last check: 2007-10-22)
		The signals from the decaying alpha particles were fed to the 4096-channel analyzer, and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded.
		The count data were analyzed and tests for randomness on a sample indicate that the device is a highly reliable source of truly random numbers.
		Random numbers from the tape are read from tape unit 13.
	www.nea.fr /abs/html/nesc0843.html (410 words)

	American Mathematical Monthly, The: What is a random sequence? (Site not responding. Last check: 2007-10-22)
		In contrast, the uses of notions of randomness are as old as civilization itself.
		One classical example2 is the `gambler's fallacy': the common (false) belief that, after a sequence of losses in a game of chance, there will follow a sequence of gains, and vice versa, in a kind of self-compensation.
		For example, a sequence of coin tosses looks very irregular, and no matter how many times we've tossed the coin, say a thousand times, no one seems to be able to predict the outcome of the next toss.
	www.24hourscholar.com /p/articles/mi_qa3742/is_200201/ai_n9046353 (1262 words)

	METHOD OF SYNCHRONISING THE PSEUDO-RANDOM BINARY SEQUENCE IN A DESCRAMBLER (EP0524235B1) (Site not responding. Last check: 2007-10-22)
		The codewords are converted to a serial bit-stream and scrambled using a PRBS (pseudo-random binary sequence) from a PRBS generator (4).
		At a receiver the serial data is descrambled using a corresponding binary sequence from a PRBS generator (5) matched to that in the transmitter.
		The descrambled data is decoded in a decoder (6) in synchronism with the binary sequence in the generator (5) thereby maintaining word alignment between the transmitter and the receiver.
	www.delphion.com /details?&pn=EP00524235B1 (232 words)

	On Random Sequence Multisets for Synchronous Code-Division Multiple-Access Channels - Grant, Alexander (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: The effect of using randomly selected sequence multisets for the uplink of a synchronous code-division multiple-access channel is considered.
		A tight lower bound on the expected value of the sum capacity over the ensemble of randomly selected sequence multisets is given.
		For large systems, the sum rate penalty for using randomly selected multisets is shown to be at most 1 nat and to vanish as the number of users becomes large, compared to the sequence length.
	citeseer.ist.psu.edu /grant98random.html (475 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		we might say, for example, that a random sequence of 0s and 1s, would be a sequence generated by repeatedly tossing a fair coin and recording a 0 for each head and a 1 for each tail.
		For a pseudo-random sequence to be acceptable for use in place of a truly random sequence, the pseudo-random sequence must pass a sufficient number of statistical tests that would also be passed by the truly random sequence.
		If the pseudo-random sequence fails to pass the same set of tests, then the numbers within the pseudo-random sequence are not sufficiently random to be useful for the purpose at hand.
	longwood.cs.ucf.edu /courses/cop3503h/day12.doc (3383 words)

	Coincidences: Remarkable or Random? (Skeptical Inquirer / September 1998)
		In a random selection of twenty-three persons there is a 50 percent chance that at least two of them celebrate the same birthdate.
		Since the decimal digits of p are random, we may simulate a random sequence of heads and tails in coin tossing by assigning even digits to heads and odd digits to tails.
		If someone finds a pattern combing random data, he or she may use it as a hypothesis for investigation of more data but should never make a general conclusion from it.
	www.csicop.org /si/9809/coincidence.html (4018 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Random Numbers and Pseudo-random Numbers You probably already have some idea of what mean when we say that a number is random.
		It is probably more useful at this point to consider a sequence as random if knowing the first n terms of the sequence, we are not able to predict (with 100 mod accuracy) the (n+1)st term.
		The expected average of all the generated numbers is 499.5 We could generate a sequence of random numbers that satisfy these properties by getting an initial clock time in milliseconds and adding one to this number on each successive call (although this won’t be very random).
	longwood.cs.ucf.edu /courses/cop3503c-03/day13.doc (3357 words)

	Random Number Generators
		If the generator is run with the same values of the parameters, and the same seed, it will generate a sequence that's identical to the previous one.
		Of course one may want random numbers not as integers in a given range, but for example as uniformly distributed real numbers in a certain interval, or perhaps as real numbers of (almost) arbitrary size, but clustered around the origin.
		The sequence generated by () isn't random* at all, so there is no good random number generator of that form.
	www.math.utah.edu /~alfeld/Random/Random.html (1373 words)

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