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	Variable - Wikipedia, the free encyclopedia
		Variables are generally distinct from parameters, although what is a variable in one context may be a parameter in another.
		In mathematical statistics, 'variable' has a technical meaning - random variables are defined in the mathematical context of measure theory as measurable functions from a probability space to a measurable space.
		By contrast, it is permissible for a variable binding to extend beyond its scope, as occurs in Lisp closures and C static variables.
	en.wikipedia.org /wiki/Variable (2383 words)

	Encyclopedia :: encyclopedia : Random variable (Site not responding. Last check: 2007-10-31)
		A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result.
		Unlike the common practice with other mathematical variables, a random variable cannot be assigned a value; a random variable does not describe the actual outcome of a particular experiment, but rather describes the possible, as-yet-undetermined outcomes in terms of real numbers.
		Mathematically, a random variable is defined as a measurable function from a probability space to some measurable space.
	www.hallencyclopedia.com /Random_variable (1186 words)

	Almost surely - Wikipedia, the free encyclopedia
		For example, imagine throwing a dart at the unit square (i.e., selecting a random point within the square); the probability that the dart lands in any subregion of the square is the area of that subregion.
		The area of the diagonal of the square is zero, so the probability that the dart lands exactly on the diagonal is zero; however, the diagonal is not the empty set; a point on the diagonal is no less probable than is any other point at which the dart could land.
		In measure theoretic probability theory these two types of random variable are not identical, but for practical purposes they are equivalent, since if a constant random variable X and an almost surely constant random variable Y represent the same constant c, then they share the same cumulative distribution functions.
	en.wikipedia.org /wiki/Almost_surely (620 words)

	Random Variables - VARIANCE OF A RANDOM VARIABLE (Site not responding. Last check: 2007-10-31)
		The variance of a random variable can be thought of this way: the random variable is made to assume values according to its probability distribution, all the values are recorded and their variance is computed.
		The variance of the function g(X) of the random variable X is the variance of another random variable Y which assumes the values of g(X) according to the probability distribution of X. Denoted by Var[g(X)], it is calculated as
		Similarly, the variance of the sum or difference of a set of independent random variables is simply the sum of the variances of the independent random variables in the set.
	library.advanced.org /10030/5rvvoarv.htm (429 words)

	[No title]
		The expected value of a random variable is analogous to the mean of a list: It is the balance point of the probability histogram, just as the mean is the balance point of the histogram of the list.
		As a consequence of the Law of Large Numbers, if a discrete random variable is observed repeatedly in independent experiments, the fraction of experiments in which the random variable equals any of its possible values is increasingly likely to be close to the probability that the random variable equals that value.
		The mean of the observed values of the random variable in repeated independent experiments is thus increasingly likely to be close to a weighted average of the possible values, where the weights are the probabilities of the values.
	www.stat.berkeley.edu /users/stark/SticiGui/Text/ch13.htm (4863 words)

	Expected value: expected monetary value, expected value perfect information, expected value theory
		In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value").
		The moments of some random variables can be used to specify their distributions, via their moment generating functions.
		To empirically estimate the expected value of a random variable, one repeatedly measures observations of the variable and computes the arithmetic mean of the results.
	wikipedia.pavelreich.com /wiki/Expected_value (937 words)

	AMS 311
		Random Variables: definition of random variable; cumulative distribution function.
		Expectation of a Function of a Random Variable
		Let X be a discrete random variable with set of possible values A and probability function p(x), and let g be a real-valued function.
	www.ams.sunysb.edu /~dorothy/handout11.html (220 words)

	RandomVariables - PineWiki
		Random sets and structures: Suppose that we have a set T of n elements, and we pick out a subset U by flipping an independent fair coin for each element to decide whether to include it.
		Expectation tells you the average value of a random variable but it doesn't tell you how far from the average the random variable typically gets: the random variable X = 0 and Y = +-1,000,000,000,000 with equal probability both have expectation 0, though their distributions are very different.
		Unlike Markov's inequality, which can only show that a random variable can't be too big too often, Chebyshev's inequality can be used to show that a random variable can't be too small, by showing first that its expectation is high and then that its variance is low.
	pine.cs.yale.edu /pinewiki/RandomVariables (2266 words)

	Random Variables
		A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon.
		A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........
		Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.
	www.stat.yale.edu /Courses/1997-98/101/ranvar.htm (1029 words)

	Statistical Review with formula of, and rules for the mean, variance, covariance, correlation coefficient
		Multiplying a random variable by a constant increases the variance by the square of the constant.
		The variance of the sum of two or more random variables is equal to the sum of each of their variances only when the random variables are independent.
		The covariance of a variable with itself is the variance of the random variable.
	www.kaspercpa.com /statisticalreview.htm (548 words)

	Linear Polynomial of a Random Vector
		A linear polynomial of a random vector is a random variable defined as a linear polynomial of some random vector.
		Suppose a random variable Z is equal to the sum of two other random variables A and B which are related by the functional relationship B = A
		chi-squared distribution If you square a normal random variable, the result is a chi-squared random variable.
	riskglossary.com /articles/linear_polynomial_of_a_random_vecrtor.htm (445 words)

	Symmetrization of Binary Random Variables (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		Abstract: A random variable Y is called an independent symmetrizer of a given random variable X if (a) it is independent of X and (b) the distribution of X + Y is symmetric about 0.
		78.4%: Symmetrization Of Binary Random Variables - Abram Kagan Colin
		7 Decomposition of Random Variables and Vectors (context) - Linnik, Ostrovskii - 1977
	citeseer.ist.psu.edu /226212.html (325 words)

	Random Variables and Distributions
		Consider the discrete random variable of the sum of pips on two rolled dies.
		If a random sample is taken, as our sample becomes larger, it becomes clear that the random variable, x takes on any integer value between two and twelve, inclusive.
		Of course, random variables being what they are, in theory one could roll a million sixes in a row.
	www.andrews.edu /~calkins/math/webtexts/prod08.htm (1403 words)

	Symmetrization Of Binary Random Variables (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		A random variable Y is called an independent symmetrizer of a given random variable X if (a) it is independent of X and (b) the distribution of X + Y is symmetric about 0.
		73.6%: Symmetrization of Binary Random Variables - Kagan, Mallows, Shepp (1999)
		68.4%: Symmetrization Of Binary Random Variables - Abram Kagan Colin
	citeseer.ist.psu.edu /251617.html (329 words)

	An Introduction to Random Variables (Part 1)
		Uppercase letters will be used to represent generic random variables, whilst lowercase letters will be used to represent possible numerical values of these variables.
		It is often of great interest to measure the extent to which a random variable X is dispersed.
		Similarly, the discrete random variables X and Y are called independent if the numerical value of X does not affect the distribution of Y.
	www.easymeasure.co.uk /randomvariables1.aspx (1056 words)

	Spatial memory and food searching mechanisms of cattle by E.A. Laca (Site not responding. Last check: 2007-10-31)
		Steers in constant random and constant clumped used long-term spatial memory to return to food locations, and ignored areas where no food was found (P < 0.01).
		Conversely, steers in variable random used a strategy based on avoidance of locations already visited within sessions.
		Thus, in constant random and constant clumped food search was more efficient (P < 0.01) and concentrated in certain areas, whereas in variable random it was less efficient and more evenly distributed over the whole area.
	uvalde.tamu.edu /jrm/jul98/laca.htm (370 words)

	$RANDOM: generate random integer
		# Changing the formula to use abs(max-min)+1 will still produce #+ correct answers, but the randomness of those answers is faulty in #+ that the number of times the end points ($min and $max) are returned #+ is considerably lower than when the correct formula is used.
		RANDOM=$$ # Reseed the random number generator using script process ID. PIPS=6 # A die has 6 pips.
		True "randomness," insofar as it exists at all, can only be found in certain incompletely understood natural phenomena such as radioactive decay.
	www.tldp.org /LDP/abs/html/randomvar.html (1838 words)

	Random variables handout (Site not responding. Last check: 2007-10-31)
		Or, especially confusingly, the variance of a single roll of a die.
		When we represent random variables mathematically, the idea is to consider all the possibilities that could occur (even though only one actually will).
		So when we consider the mean of a single random variable, think of it as the "mean of possibilities" that the random variable could turn out to be.
	www.sscnet.ucla.edu /ssc/labs/brenner/econ40/randomvar.htm (180 words)

	Assignment for January 25, 2006
		E(X + Y) = E(X) + E(Y), where X and Y are random variables and E(X) denotes the expected value (=expectation = mean) of the random variable X. If c is a constant and X is a random variable, then E(cX) = cE(X).
		If X is a constant random variable (with constant value c), then E(X) = c.
		Use the definition of variance above and the facts about expected value above to derive a formula for Var(cX), where c is a constant.
	www.ma.utexas.edu /~mks/358Ksp06/jan25.html (566 words)

	Expected Value
		In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value").
		For example, suppose X is a discrete random variable with values xi and corresponding probabilities pi.
		Now consider a weightless rod on which are placed weights, at locations xi along the rod and having masses pi (whose sum is one).
	www.craps.online.gambling.name /expected_value.html (755 words)

	[No title]
		Let X be a discrete random variable; then for constants a and b we have that EMBED Equation.COEE2 and EMBED Equation.COEE2 Definition Let X and Y be two random variables and (be a given point.
		Calculate the expected winning and variance of winning for a strategy: bet $5 on red at first play; if loss, bet $10 on red on second play; if two losses in a row, bet $20 on red on third play; and so on.
		Problem: Let X be an indicator variable; that is, it takes the value 1 with probability p and the value 0 with probability 1-p.
	www.ams.sunysb.edu /~finchs/lec14.doc (1360 words)

	PHYS 381/504: Modern Physics Measurements
		In dealing with random variables, we are lead to the probability densities for those variables.
		This quantity is the correlation function or autocorrelation function of the random process in question.
		Given a random variable as a function of time acquired at a sampling frequency
	www.yale.edu /physics/PHYS381_504/Random-variables/index.html (610 words)

	[No title]
		The expectation of a constant, c, is the constant.E(c) = c Rule 2.
		Multiplying a random variable by a constant value, c, multiplies the expected value or mean by that constant.E(cX) = cE(X) Rule 4.
		Multiplying a random variable by a constant increases the variance by the square of the constant. INCLUDEPICTURE "http://www.kaspercpa.com/images/Mathtype/varrule3.gif" \* MERGEFORMATINET Rule 4.
	bear.cba.ufl.edu /demiroglu/fin4504fall2004/Articles/Statistics.doc (913 words)

	RandomVariableTable (SOCR API Specification)
		This class defines a basic table for displaying the distribution and moments and the empirical distribution and moments for a specified random variable.
		This general constructor creates a new random variable table with a specified random variable.
		The name of the random variable and the structure of the table may have changed.
	socr.stat.ucla.edu /docs/edu/uah/math/devices/RandomVariableTable.html (319 words)

	nts01 (Site not responding. Last check: 2007-10-31)
		These notes are a commentary on the text and are to be read along with it.
		be the covariance matrix of a random vector X with mean vector
		that is to say, there is a variate which is degenerate in this sense
	www.uic.edu /classes/bstt/bstt580/jw4e/nts02.htm (98 words)

	The random-variable canonical distribution
		Whereas Gibbs' theory is based upon a consideration of systems subject to dynamical law, the present analysis relies neither on the classical equations of motion nor makes use of any a priori probability of a complexion; rather, it makes avail of the basic algebra of random variables and, specifically, invokes the law of large numbers.
		Thereby, a canonical distribution is derived which describes a macrosystem in probabilistic, rather than deterministic, terms, and facilitates the understanding of energy fluctuations which occur in macrosystems at an overall constant ensemble temperature.
		A discussion is given of a modified form of the Gibbs canonical distribution which takes full account of the effects of random energy fluctuations.
	stacks.iop.org /0305-4470/34/2913 (309 words)

	An Introduction to Random Variables (Part 2)
		This article follows on from An Introduction to Random Variables (Part 1).
		Here, fundamental results regarding the expectation and variance of random variables (discrete or continuous) are stated and proved.
		The proof of (3) is first presented for discrete random variables X and Y.
	www.easymeasure.co.uk /randomvariables2.aspx (311 words)

	Normal Random Variable
		If we take a an affine transformation of a standard Normal random variable: Y=aZ+b the new density of Y is
		This is called the Normal variable with parameters, b and a
		In general if you have a Normal random variable with parameters
	www-stat.stanford.edu /~susan/courses/s116/node96.html (107 words)

	33.3.1.0.3 Delay and Loss Modules
		A constant random variable is created; it will generate random delivery times using the accumulative delay as an estimate of the average delay.
		A new delay module is created with the end-to-end bandwidth characteristics, and the random variable generator provides the delay estimates.
		The delay module in inserted into the session helper and interposed between the helper and the receiver.
	www.isi.edu /nsnam/ns/doc-stable/node463.html (156 words)

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