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Topic: Probability density function

	Probability density function - Wikipedia, the free encyclopedia
		A probability density function is non-negative everywhere and its integral from −∞ to +∞ is equal to 1.
		In the field of statistical physics, a non-formal reformulation of the relation above between the derivative of the cumulative distribution function and the probability density function is generally used as the definition of the probability density function.
		The definition of a probability density function at the start of this page makes it possible to describe the variable associated with a continuous distribution using a set of binary discrete variables associated with the intervals [a; b] (for example, a variable being worth 1 if X is in [a; b], and 0 if not).
	en.wikipedia.org /wiki/Probability_density_function (898 words)

	Probability amplitude - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In quantum mechanics, a probability amplitude is a complex-valued function that describes an uncertain or unknown quantity.
		For a probability amplitude ψ, the associated probability density function is ψ*ψ, which is equal to ψ
		Probability amplitudes which are not square integrable are usually interpreted as the limit of a series of functions which are square integrable.
	en.wikipedia.org /wiki/Probability_amplitude (409 words)

	1.3.6.2. Related Distributions
		Probability distributions are typically defined in terms of the probability density function.
		The hazard function is the ratio of the probability density function to the survival function, S(x).
		The cumulative hazard function is the integral of the hazard function.
	www.itl.nist.gov /div898/handbook/eda/section3/eda362.htm (597 words)

	Kids.net.au - Encyclopedia Density - (Site not responding. Last check: 2007-11-06)
		In the SI system of units, density is measured as kg/m³ (kilogram per cubic metre), but many people use the more convenient g/cm³ (gram per cubic centimetre[?]) or (equivalently) kg/l (kilograms per litre).
		By definition, then, the relative density (or RD) of water is 1, and the RD of osmium is about 22.
		Density may denote how much of a certain substance, object or occurrence is present per unit area or volume.
	www.kidsseek.com /encyclopedia-wiki/de/Density (487 words)

	Probability Density Function (Site not responding. Last check: 2007-11-06)
		Typically, the probability density function is viewed as the shape of the distribution.
		The area below the probability density function to the left of a given value, x, is equal to the probability of the random variable represented on the x-axis being less than the given value x.
		Note that as the width of the interval decreases, the area, and thus the probability of the length falling in the interval decreases.
	www.engineeredsoftware.com /lmar/density.htm (391 words)

	Ec305 Lecture notes
		This is a probability density function of the standard normal distribution.
		Probability is the area under the density curve.
		The cumulative distribution function is the probability that the random variable will be less or equal to a specific value.
	www.bu.edu /econ/faculty/kyn/newweb/Ec305/ec305_lecture_notes_3.htm (317 words)

	Functions and CALL Routines : PDF
		The PDF function for the beta distribution returns the probability density function of a beta distribution, with shape parameters a and b, which is evaluated at the value x.
		The PDF function for the chi-squared distribution returns the probability density function of a chi-squared distribution, with df degrees of freedom and noncentrality parameter nc, which is evaluated at the value x.
		The PDF function for the F distribution returns the probability density function of an F distribution, with ndf numerator degrees of freedom, ddf denominator degrees of freedom, and noncentrality parameter nc, which is evaluated at the value x.
	www.asu.edu /it/fyi/unix/helpdocs/statistics/sas/sasdoc/sashtml/lgref/z0270634.htm (1051 words)

	Probability Density Function of climate time series (Site not responding. Last check: 2007-11-06)
		probability of the random variable to be less than or equal to a certain value a is equal to the integral of the PDF for values of the variable from negative infinity to a.
		probability of the random variable to be between a and b equal to the integral of the PDF for values of the variable from a to b.
		probability of the random variable to be greater than (to exceed) a certain value a equal to the integral of the PDF for values of the variable from a to positive infinity (Probability of exceedance).
	www.nws.noaa.gov /om/csd/pds/pcu2/res/students/Stats/part1/BS_pdf.htm (401 words)

	Problem Distribution (Site not responding. Last check: 2007-11-06)
		The integral of the probability function from the lower to the upper bound of the range, which is the area under that portion of the curve, gives the probability that the outcome is in that range.
		For example, the probability that the random velocity in the x direction of a dust particle is between 3.0 mm/sec and 4.0 mm/sec is the integral of the probability density function from 3.0 to 4.0.
		For the probability density function with graph in Figure 3, give the probability that the random number falls between 0.2 and 0.7.
	www.wofford.edu /ecs/ScientificProgramming/probdistribution/material.htm (3553 words)

	Calculus and Probability 2
		A probability density function (or probability distribution function) is a function f defined on an interval (a, b) and having the following properties.
		The uniform density function on the interval [a, b] is the constant function defined by
		There is a theorem in probability theory called the Central Limit Theorem that says that a large class of probability density functions may be approximated by normal density functions.
	www.zweigmedia.com /ThirdEdSite/cprob/cprob2.html (1950 words)

	Statistics Glossary - Probability
		Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1.
		For a continuous random variable, the cumulative distribution function is the integral of its probability density function.
		The probability density function of a continuous random variable is a function which can be integrated to obtain the probability that the random variable takes a value in a given interval.
	www.cas.lancs.ac.uk /glossary_v1.1/prob.html (3540 words)

	Moment-generating function - Wikipedia, the free encyclopedia
		The moment-generating function generates the moments of the probability distribution, and thus uniquely defines the distribution of the random variable.
		Regardless of whether the probability distribution is continuous or not, the moment-generating function is given by the Riemann-Stieltjes integral
		Related to the moment-generating function are a number of other transforms that are common in probability theory, including the characteristic function and the probability-generating function.
	en.wikipedia.org /wiki/Moment-generating_function (202 words)

	Probability density functions, discrete and continuous
		The probability of the sample at (-3, 2) is p(-3, 2) = 0.238%, the sample at (-3, -2) is p(-3, -2) = 1.19%, and p(3,-2) = 8.33%.
		The probability of the small square is the probability per unit area calculated at (x,y) multiplied by the area of the square, dx times dy.
		In one dimension, the probability density is a function of one variable, p(x).
	www.sirus.com /users/mjake/probdens.html (2729 words)

	Probability density function - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, a probability density function serves to represent a probability distribution in terms of integrals.
		For example, the uniform distribution on the interval [0,1] has probability density f(x) = 1 for 0 ≤ x ≤ 1 and zero elsewhere.
		Two densities f and g for the same distribution can only differ on a set of Lebesgue measure zero.
	encyclopedia.learnthis.info /p/pr/probability_density_function.html (320 words)

	Improper integrals and probability density functions
		For example, the probability that a single flip of a coin produces tails is 50%.
		Probably the most important distribution is the normal distribution, widely referred to as the bell-shaped curve.
		It's reasonable to model the probability of failure of these lightbulbs by an exponential density function with mean 1000.
	www.math.wpi.edu /Course_Materials/MA1023C05/probability/node1.html (1197 words)

	Interval Timer - Student's Guide
		This probability is related to the area under the probability density function as shown in Figure 20.
		The probability that the value on a ball is between 0 and 1 is 1.
		The probability that the value is between 0.3 and 0.5 is the area under the curve between 0.3 and 0.5 as shown in Figure 20(b).
	www.uml.edu /Dept/EE/EASNE/2s2.htm (2125 words)

	PlanetMath: density function
		If the density function for a random variable is known, we can calculate the probability of
		For a more formal approach using measure theory, look at probability distribution function entry.
		This is version 9 of density function, born on 2002-09-11, modified 2005-02-21.
	planetmath.org /encyclopedia/Density.html (145 words)

	ipedia.com: Density Article (Site not responding. Last check: 2007-11-06)
		Density is a measure of mass per unit of volume.
		Density (symbol: ρ - Greek: rho) (ISO 31: volumic mass) is a measure of mass per unit of volume.
		= 1 kg/L. In Imperial units or U.S. customary unit, the unit of density is the pound/cubic foot.
	www.ipedia.com /density.html (563 words)

	PlanetMath: probability distribution function
		The main feature of a probability distribution function is that it induces a probability measure
		See Also: measure, stochastic matrix, discrete density function, distribution function, density function, area under Gaussian curve
		This is version 5 of probability distribution function, born on 2002-04-29, modified 2004-11-30.
	planetmath.org /encyclopedia/Distribution.html (169 words)

	Continuous Distributions
		Unlike the discrete case, the existence of a density function for a continuous random variable is an assumption that we are making.
		Moreover, unlike the discrete case, the density function of a continuous random variable is not unique.
		The density function of X, of course, is based on the underlying probability measure P for the experiment.
	www.fmi.uni-sofia.bg /vesta/Virtual_Labs/dist/dist2.html (1079 words)

	Calculus II (Math 2414) - Applications of Integrals - Probability
		Probability density functions can be used to determine the probability that a continuous random variable lies between two values, say
		Note the change in limits on the integral. The function is only non-zero in these ranges and so the integral can be reduced down to only the interval where the function is not zero.
		Probability density functions can also be used to determine the mean of a continuous random variable. The mean is given by,
	tutorial.math.lamar.edu /AllBrowsers/2414/Probability.asp (450 words)

	Normal Distribution (Site not responding. Last check: 2007-11-06)
		The standard normal probability density function has a mean of 0 and a standard deviation of 1.
		The probability of the strength being between 295 and 310 is 1-0.0228-0.1587 = 0.8185.
		The probability density function of the voltage of the individual batteries and of the average of nine batteries is shown in the figure below.
	www.engineeredsoftware.com /nasa/normal.htm (946 words)

	A probability density function (Site not responding. Last check: 2007-11-06)
		Notice that the scales an the X and Y axes are not the same and there is a break in the X-axis between 0 and 11.975.
		Notice also that the arera under the curve, that part shaded yellow, is 1 as it must be for a probability density function.
		On the diagram that is the area under the density function, between 12 and 12.05, the region shaded red in the diagram below.
	mathcentral.uregina.ca /QQ/database/QQ.09.03/husain1.html (247 words)

	Calculus and Probability 3
		Statisticians use the variance and standard deviation of a continuous random variable X as a way of measuring its dispersion, or the degree to which is it "scattered." The definitions are as follows.
		Again, a small standard deviation means that the values of X will be close to the mean with high probability, while a large standard deviation means that the values may wander far away with high probability.
		If a probability curve has as much area to the left of the mean as to the right, then the mean is equal to the median.
	www.zweigmedia.com /ThirdEdSite/cprob/cprob3.html (1588 words)

	ME290M, Spring 1999, On-Line Resources
		There is only one probability density function for the "fair" Wheel of Fortune that will satisfy equation [2] and is numerically the same for all values of x, that is Pr(x=xo) =1 for all 1 · xo · 1.
		Moments of probability density functions are a generalization of the concept of expected value.
		The third moment is related to the symmetry of the probability density function and is sometimes referred to as the skewness of the probability density function.
	best.me.berkeley.edu /~aagogino/me290m/s99/continuous.variables/continuous.html (535 words)

	LHAPDF Theory
		As the PDF uncertainties will affect all areas of phenomenology at hadron colliders, a clear mathematical framework of a PDF fit is essential [1].
		The most crucial property of the prior function is that it defines the functional integral by imposing smoothness constraints to make the number of degrees of freedom become finite.
		(8), as the probability density function of the observable is the average of the response function over the unweighted PDFs.
	vircol.fnal.gov /theory.htm (2159 words)

	Probability Densities and Distributions
		Constant probability density over the entire range of the independent variable is the exception, not the rule.
		Unlike probabilities corresponding to exact values of continuous variable, probabilities over a range of the independent variable can be large enough to have some meaning.
		Instead, as we have seen earlier, the density of probabilities of quitting for var is an exponential decay (more like our second example of probability density).
	www.holycross.edu /departments/biology/kprestwi/behavior/ESS/warAtt_abtProbDensityFunc.html (3249 words)

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