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Topic: Law of large numbers

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	Law of large numbers - Uncyclopedia
		The law of large numbers is a term in political theory first coined by Thomas Hobbes in his famous political text, Leviathan.
		Hobbes used this term to describe the behavior of numbers in the state of nature; he argued that, left to themselves, without a general theory of mathematics to overawe them all, numbers would descend into a war of all against all where only the largest numbers survived.
		The usual use in debate is along the political speech formula of "Your (war/policy) has (killed/injured/maimed/widowed/economically ruined) (large number) (people/soldiers/immigrants/minorities)" A notable opponent of the law of large numbers was Josef Stalin, stating that "the death of one man is a tragedy.
	uncyclopedia.org /wiki/Law_of_large_numbers (357 words)

	Law of large numbers - Wikipedia, the free encyclopedia
		The law of large numbers is a fundamental concept in statistics and probability that describes how the average of a randomly selected sample from a large population is likely to be close to the average of the whole population.
		The phrase "law of large numbers" is also sometimes used in a less technical way to refer to the principle that the probability of any possible event (even an unlikely one) occurring at least once in a series increases with the number of events in the series.
		A consequence of the weak law of large numbers is the asymptotic equipartition property.
	en.wikipedia.org /wiki/Law_of_large_numbers (1103 words)

	PlanetMath: strong law of large numbers
		Kolmogorov's strong law of large numbers theorems give conditions on the random variables under which the law is satisfied.
		"strong law of large numbers" is owned by Koro.
		This is version 8 of strong law of large numbers, born on 2002-12-08, modified 2006-09-28.
	planetmath.org /encyclopedia/StrongLawOfLargeNumbers.html (114 words)

	PlanetMath: Kolmogorov's strong law of large numbers
		The strong law of large numbers holds if one of the following conditions is satisfied:
		Cross-references: variance, strong law of large numbers, expectations, finite, random variables, independent, sequence
		This is version 4 of Kolmogorov's strong law of large numbers, born on 2002-12-08, modified 2006-09-28.
	planetmath.org /encyclopedia/KolmogorovsStrongLawOfLargeNumbers.html (83 words)

	Hussman Funds - Weekly Market Comment: October 25, 2004 - Law of Large Numbers
		The law of large numbers basically says that if you make repeated, independent draws from a given “population,” the average value of your sample will approach the true population average as the sample size becomes large.
		That said, the law of large numbers suggests that short-term returns should eventually begin to average out toward the long-term average if all is well.
		Notice that the law of large numbers requires the samples to be “independent.” Following a particular investment approach over numerous time periods would qualify those samples as being reasonably independent, for example.
	www.hussmanfunds.com /wmc/wmc041025.htm (2136 words)

	Probability Theory - The Laymans guide to probability (Site not responding. Last check: 2007-10-13)
		An understanding of the law of the large numbers leads to a realisation that what appear to be fantastic improbabilities are not remarkable at all but, merely to be expected.
		Yet when we that the number of bridge hands dealt since the game was invented is doubtless many times the large number quoted, it would be surprising if a hand of 13 spades had never been dealt legitimately.
		This occurs in horse racing, where the number of four-horse accumulators which can be taken from a total of eight selections might be required, or in selecting draws for a treble-chance football pool, where perhaps the number of combinations of eight draws from ten selections are needed.
	www.probabilitytheory.info - !http: //www.peterwebb.co.uk/probability.htm (6661 words)

	Law of Truly Large Numbers - Wikipedia, the free encyclopedia
		Critics of this law claim deny its application to supernatural events on the basis that they are by definition "above nature".
		This way, the law is still valid as an explanation for the occurrence of highly improbable or coincident events, implying that there is no super-natural cause to be suspected in those occurrences.
		Any supposed "supernatural" events are then interpreted as a result of physical laws that we are currently unaware of or do not understand properly, so the Law of Truly Large Numbers should apply to them as well.
	en.wikipedia.org /wiki/Law_of_Truly_Large_Numbers (539 words)

	The Law of Large Numbers by Dr. Gary Goodman
		The law states, that "In any chance event, when the event happens repeatedly, the actual results will tend to be the calculated, or planned, results." In essence, this means that repeated actions, over time, will, almost without exception, produce the results we seek.
		While the law of large numbers has been applied to fields such as math and science for several decades, its power has just recently begun to be applied to the fields of business and personal growth.
		Today, people from all walks of life are using the law of large numbers to achieve their highest objectives, with great confidence and complete peace of mind.
	www.nightingale.com /pg~Product~Law_Large_Numbers.asp (494 words)

	Law of Truly Large Numbers
		The law of truly large numbers says that with a large enough sample many odd coincidences are likely to happen.
		The number is actually likely to be larger, since we tend to dream about things that legitimately concern or worry us, and the data of dreams is usually vague or ambiguous, allowing a wide range of events to count as fulfilling our dreams.
		Given the fact that there are billions of people and the possible number of meaningful coincidences is millions of billions, it is inevitable that many people will experience some very weird and uncanny coincidences every day.
	skepdic.com /lawofnumbers.html (1394 words)

	the riddle revealed (Site not responding. Last check: 2007-10-13)
		First I might note that in math texts, their really is no such thing as literally the law of large numbers.
		Then what the law of large numbers states is that as the number of rolls approaches infinity - the observed proportion of sevens will approach the value of p=1/6.
		The seemingly large effect of what we thought to be 66.67 owed tosses, actually only shows up as a difference of say.0000000001 from the theoretical value of p=1/6.
	www.math.montana.edu /~hodgson/largenumbers.htm (349 words)

	SPREADSHEET SIMULATION OF THE LAW OF LARGE NUMBERS Mathematics and Computer Education - Find Articles
		This remarkable fact, known as the law of large numbers, holds true if we draw samples from a population of discrete or continuous values, or draw them from a population with a skewed distribution.
		The purpose of this article is to present an Excel workbook to use in an undergraduate introductory statistics class to simulate an application of the law of large numbers.
		Students see that different simulation runs create different paths from left to right in the graph, but the law of large numbers says that whatever path we get, the long run average will always settle to the level of the population mean.
	www.findarticles.com /p/articles/mi_qa3950/is_200510/ai_n15868737 (915 words)

	cell project space : The Law of Large Numbers
		By operating within the constraints that science has filtered for them all 7 artists invited to exhibit at Cell, in some way, address the laws of physics with their mutation of geometry or exploding structures using mathematics, repetition or pattern to greater or lesser degree.
		They present a universe that is at once deterministic and obeys the fundamental laws of physics but is capable of disorder, complexity and unpredictability.
		The show connects our everyday experiences to the laws of nature by revealing the subtle relationships between simplicity and complexity and between orderliness and randomness.
	www.cell.org.uk /show/lawoflargenumbers (529 words)

	Myswizard » Law of large numbers
		Although the repetition of dangerous practices leads to the conclusion that there is a higher likelihood of having a negative ending, repetition of higher spiritual practices on the journey to enlightenment, increase the odds for leaps of consciousness.
		For example, the average weight of 10 apples taken from a barrel of 100 apples is probably closer to the “real” average weight than the average weight of 3 apples taken from that same barrel.
		In particular, it permits precise measurement of the likelihood that an estimate is close to the “right” number.
	www.myswizard.com /2006/09/27/law-of-large-numbers (652 words)

	The Sample Mean and the Law of Large Numbers
		Note that the mean of the sample mean stays the same, but the standard deviation of the sample mean decreases (as we now know, in inverse proportion to the square root of the sample size).
		In the simulation of the binomial coin experiment, the random variable is the number of heads.
		In the simulation of the matching experiment, the random variable is the number of matches.
	www.ds.unifi.it /VL/VL_EN/sample/sample2.html (820 words)

	AZCompuguy - ScottoBobScotto - Law of Numbers
		A common story is the one about having a dream or thought about the death of a friend or relative and then receiving a phone call five minutes later about the unexpected death of that very person.
		I cannot always explain such specific incidents, but a principle of probability called the Law of Large Numbers shows that an event with a low probability of occurrence in a small number of trials has a high probability of occurrence in a large number of trials.
		So the total number of events that happen to us is about thirty thousand per day, or about a million per month.
	www.azcompuguy.com /numbers.htm (590 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		However, if we flipped the coin 10 million times—a large number of times—the calculated probability of 50% heads and 50% tails would be extremely accurate.
		Insurance companies cannot predict who will die when, but by using data about a large number of people, they can predict with reasonable accuracy how many people in a given population are likely to die during a certain period of time.
		And thus, the law of large numbers aids insurance companies in determining appropriate premium charges to ensure they can maintain financial strength while paying out claims.
	www.nmfn.com /tn/netserv--personal--page_law_large_num (290 words)

	Re: The Law of Large Numbers (Site not responding. Last check: 2007-10-13)
		These expression is used to refer to two asymptotic results known as the Strong Law of Large Numbers and the Weak Law of Large Numbers.
		The first 400 rolls (or even the first 1,000,000 rolls) are irrelevant for asymptotic results as their effect is wiped out by the zillions of rolls which are needed for the "long run".
		Re: The Law of Large Numbers Pete Moss 01:06:12 6/27/97 (
	www.bjmath.com /bjmath/Independ/bisser.htm (213 words)

	Brad DeLong's Semi-Daily Journal: The Law of Large Numbers (Site not responding. Last check: 2007-10-13)
		law of large numbers tells us that the sample average you compute will converge to the true population average at a frighteningly rapid speed.”
		But it becomes far too easy for anyone to dismiss anything by claiming bias, which disheartens me, as I just brought this up to a number of intelligent friends and they responded by saying 'but you can't be sure you've eliminated bias!' as though it was a mantra for avoiding statistical results they dont' like.
		As the number of variables increases, the difficulty of randomization increases with it.
	delong.typepad.com /sdj/2005/07/the_law_of_larg.html (3145 words)

	Law.com - Responding to Critics, 9th Circuit Will Try Law of Large Numbers
		The question of whether an 11-judge en banc panel can adequately represent the opinions of a court with 28 judgeships (it currently has 24 active judges) has frequently come up in the debate over whether to split the 9th Circuit.
		Arthur Hellman, a professor at the University of Pittsburgh School of Law and an expert on the 9th Circuit who has studied the en banc question, said there was no need to increase the size of the panel "based on what's called game-theory results, statistical results."
		In 2000, Hellman conducted a study of whether the 11-judge panel was adequate.
	www.law.com /jsp/article.jsp?id=1128416712246 (647 words)

	Math Forum - Ask Dr. Math
		Date: 02/09/2001 at 11:31:54 From: Doctor Jordi Subject: Re: Laws of large numbers Hi Garrick - thank you for writing to Dr. Math.
		Simply stated, the law of large numbers states that if you repeat a random experiment, such as tossing a coin or rolling a die, many, many, many times, your outcomes should on average be equal to the theoretical average.
		By the law of large numbers, if you toss the coin many times, say 100, you should expect to get about the same number of heads and tails.
	mathforum.org /library/drmath/view/52799.html (371 words)

	LAW OF LARGE NUMBERS (Site not responding. Last check: 2007-10-13)
		This treatise called the Ars Conjectandi is more commonly known as The Law of Large Numbers.
		Today, this Law of Large Numbers is still of the highest usefulness in it's theories of probabilities and it's applications to insurance, statistics and the mathematical study of heredity.
		Once you see the comparison, you will understand why we say lotteries are classic examples of the Law of Large Numbers.
	www.lotteryamerica.com /suggested/law.htm (368 words)

	Law of Large Numbers System Design (2004) (Site not responding. Last check: 2007-10-13)
		We must, instead, employ the ``Law of Large Numbers'' above the device level in order to obtain predictable behavior from atomic-scale phenomena which are statistical in nature.
		At the same time, the ``Law of Large Numbers'' can also help us by providing statistical differentiation at scales smaller than those we can pattern directly or economically using lithography.
		In this chapter, we examine various applications of the ``Law of Large Numbers'' above the device level to build reliable and controllable systems from nanoscale devices and processes that only have statistically predictable behavior.
	ic.ese.upenn.edu /abstracts/llnsd_nanobook2004.html (247 words)

	360_large_law (Site not responding. Last check: 2007-10-13)
		The Law of Large Numbers says that in repeated, independent trials with the same probability p of success in each trial, the percentage of successes is increasingly likely to be close to the chance of success as the number of trials increases.
		More precisely, the chance that the percentage of successes differs from the probability p by more than a fixed positive amount, e > 0, converges to zero as the number of trials n goes to infinity, for every number e > 0.
		Note that in contrast to the difference between the percentage of successes and the probability of success, the difference between the number of successes and the expected number of successes, n×p, tends to grow as n grows.
	www.uncp.edu /home/marson/360_large_law.html (133 words)

	Law of Large Numbers
		- Weak Law of Large Numbers: the mean of a sequence of random variables converges to the population mean in probability.
		- Strong Law of Large Numbers: the mean of a sequence of random variables converges to the population mean almost sure.
		Basicly, Chebyshev's Inequality says that 75% of your data would be two times the standard deviation from the mean, and 95% three times.
	www.physicsforums.com /showthread.php?t=64351 (248 words)

	On the strong law of large numbers, Ryszard Jajte
		On the strong law of large numbers, Ryszard Jajte
		A version of the SLLN for a large class of means is proved.
		Keywords: Strong law of large numbers; logarithmic means
	projecteuclid.org /getRecord?id=euclid.aop/1046294315 (30 words)

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