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Topic: Continuous random variable

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	Continuous random variable - Wikipedia, the free encyclopedia
		While for a discrete random variable one could say that an event with probability zero is impossible, this can not be said in the case of a continuous random variable, because then no value would be possible.
		By another convention, the term "continuous random variable" is reserved for random variables that have probability density functions.
		A random variable with the Cantor distribution is continuous according to the first convention, and according to the second, is neither continuous nor discrete nor a weighted average of continuous and discrete random variables.
	en.wikipedia.org /wiki/Continuous_random_variable (215 words)

	Random variable - Wikipedia, the free encyclopedia
		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.
	en.wikipedia.org /wiki/Random_variable (1197 words)

	Statistics Glossary - random variables and probability distributions
		The (population) variance of a random variable is a non-negative number which gives an idea of how widely spread the values of the random variable are likely to be; the larger the variance, the more scattered the observations on average.
		For a continuous random variable, the cumulative distribution function is the integral of its probability density function.
		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.stats.gla.ac.uk /steps/glossary/probability_distributions.html (2101 words)

	Entropy of a Continuous Random Variable (Site not responding. Last check: 2007-10-08)
		Shannon's entropy though defined for a discrete random variable can be extended to situations when the random variable under consideration is continuous.
		It has many of the properties of discrete entropy but unlike the entropy of a discrete random variable that of a continuous random variable may be infinitely large, negative or positive (Ash, 1965 [6]).
		The entropy of a discrete random variable remains invariant under a change of variable, however with a continuous random variable the entropy does not necessarily remain invariant.
	www.mtm.ufsc.br /~taneja/book/node13.html (108 words)

	Probability density function of a Random Variable (Site not responding. Last check: 2007-10-08)
		A continuous random variable, much like its discrete counterpart, is a number that corresponds to an outcome of a non predictable event.
		Examples of continuous random variables include: the amount of rainfall during the next month, the length time you have to wait to cross a busy street, or weight of a prize pumpkin.
		Let X be the random variable from the distribution for which all values between 0 and 10 are equally likely.
	www.unca.edu /math/OnLine/Stat220/Lesson/L_MS_Cpdf.html (320 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Consequently, for continuous random variables, probabilities are calculated for a range of values, between a and b.
		Probability density function (pdf) of a continuous random variable is the line on an X versus f (x) graph.
		The Uniform Distribution If the random variable X takes on any value in a range or an interval equally likely along the range or the interval it is a uniform distribution.
	academics.vmi.edu /econ_kg/Stats/Day15EC203uniform.doc (347 words)

	MATH250 - Tutorial on discrete random variables; printable version
		A continuous random variable can take any value in an interval or in several intervals of real numbers, whereas in the case of a discrete random variable there are gaps between consecutive possible values.
		While some random variables are naturally discrete (for example, the number of siblings a person has), in many cases it is a matter of choice whether a given feature should be modelled as a discrete or a continuous random variable.
		A random variable X takes the value 0 with probability 0.5, the value 1 with probability 0.3, and the value 2 with probability 0.2.
	www.math.ohiou.edu /~just/WINTER250/randvarp.htm (1161 words)

	5.6 Continuous random variables: distribution function and density function (Site not responding. Last check: 2007-10-08)
		Many random variables observed in real life are not discrete random variables because the number of values they can assume is not countable.
		The distinction between discrete random variable and continuous random variables is usually based on the difference in their cumulative distribution functions.
		If the data represent measurements on a continuous random variable and if the amount of data is very large, we can reduce the width of the class intervals until the distribution appears to be a smooth curve.
	www.netnam.vn /unescocourse/statistics/56.htm (368 words)

	Probability density function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		For example, the continuous uniform distribution on the interval [0,1] has probability density f(x) = 1 for 0 ≤ x ≤ 1 and zero elsewhere.
		If a random variable X is given and its distribution admits a probability density function f(x), then the expected value of X (if it exists) can be calculated as
		Not every probability distribution has a density function: the distributions of discrete random variables do not; nor does the Cantor distribution, even though it has no discrete component, i.e., does not assign positive probability to any individual point.
	www.americancanyon.us /project/wikipedia/index.php/Probability_density_function (489 words)

	5. Cont. Rand. Vars.
		Continuous random variables are introduced by giving either their pdf or cdf.
		A Uniform Random Variable with parameters a and b is a continuous random variable that can assume values in any small subinterval of length d within the interval from a to b with equal probability.
		The Normal Random Variable is defined by the probability density function shown in the next section.
	www.csus.edu /indiv/j/jgehrman/courses/stat50/continuousrvs/5continuousrvs.htm (1178 words)

	September 27, 2001
		A probability model for X is given by assigning to a set of outcomes A the probability P(A) equal to the area above A and under a curve.
		A continuous random variable X is said to have a
		variance of a continuous random variable X with pdf f(x) and mean value m is
	www.mcs.drexel.edu /~omokliat/courses/math311F02/HANDOUTS/hand17.htm (378 words)

	Lecture 14 (Site not responding. Last check: 2007-10-08)
		A density function describes the distribution of a random variable as follows: The probability that x has some value between a and b is the area under the curve between a and b on the axis.
		In the example shown the probability that the random variable's observed value lies between 1 and 2 is the amount of area shaded in yellow.
		A special continuous distribution called the uniform distribution on the interval [a,b] occurs when a random variable is equally likely to take any value between a and b.
	barnyard.syr.edu /mat121/l14 (327 words)

	SurfStat.australia (Site not responding. Last check: 2007-10-08)
		So for a continuous random variable X, we describe the probability distribution by some function f(x) e.g.
		Instead for continuous random variables probabilities are associated with a range of values.
		One example of a probability density function for a continuous random variable is the uniform continuous distribution.
	www.math.grin.edu /~mooret/main/3-2-6.html (211 words)

	Discrete and continuous random variables
		The sample space for the eventis just a list containing all possible values of the random variable.This section introduces the concept of a random variable and theprobabilities associated with the various values of thevariable.
		Example: If x is a random number inthe interval [0,1], then x is a continuous random variable.
		Atechnical note is that the random numbers generated on the TI-83 arerounded to 10 decimal places, so you are really looking atdiscrete.
	www.herkimershideaway.org /apstatistics/ymmsum99/ymm771.htm (256 words)

	Expected Value of a Random Variable (Site not responding. Last check: 2007-10-08)
		To calculate and interpret the mean and variance of a continuous Random Variable.
		A continuous random variable differs from a discrete one in that it is defined over an interval.
		Thus the calculation of its mean and variance requires the tools of calculus.
	www.unca.edu /math/OnLine/Stat220/Lesson/L_MS_CExpVal.html (243 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Let T be the continuous random variable giving the time, in hours after noon, when the guard passes your office.
		Let T be the random variable that gives the time, in minutes and parts of minutes, by which the flight is late.
		Let X be the continuous random variable that gives the time, in minutes and parts of minutes, between phone calls.
	math.arizona.edu /~smj/RV2.doc (1113 words)

	[No title]
		What is important about this section is the recognition that for all continuous variables the theory related to finding the E(X), the variance and standard deviation and probability of events is essentially the same for all continuous distributions.
		It is also important to recognise that integration for the continuous random variables is the equivalent of summation for discrete random variables.
		Thus the approach for continuous and discrete random variables is essentially the same.
	www.uow.edu.au /~jimw/dipt131/DIPT131_SPSS_Note_10.doc (298 words)

	Chi square
		Any continuous random variable can be described using the MEAN and VARIANCE measures, just like any discrete random variable.
		Statistical tests performed on random variables which follow a Chi-square distribution are called “Chi-square tests”.
		For example, suppose we are trying to model the weather tomorrow using a bunch of variables: number of cars on the street right now, number of people in GSC, and amount of snow on the ground.
	www.genetics.wustl.edu /bio5488/lecture_notes_2004/chi.html (722 words)

	[No title]
		A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,........
		Typically, a Geometric random variable is the number of trials required to obtain the first failure, for example, the number of tosses of a coin untill the first 'tail' is obtained; components from a production line are tested, in turn, until the first defective item is found.
		A continuous random variable X is said to follow a Uniform distribution with parameters a and b, written X ~ Un(a,b), if its probability density function is constant within a finite interval [a,b], and zero outside this interval,
	www.cas.lancs.ac.uk /glossary_v1.1/prob2.html (1336 words)

	5.7 Numerical characteristics of a continuous random variable (Site not responding. Last check: 2007-10-08)
		be a continuous random variable with density function f(x).
		be a continuous random variable with density function f(x) and g(x) is a function of x.
		be a continuous random variable with the the expected value
	www.netnam.vn /unescocourse/statistics/57.htm (76 words)

	Module 9: Probability - Section 8 (Site not responding. Last check: 2007-10-08)
		Now suppose we have a continuous random variable X that can take any value between 2 and 5.
		So there is a difference between the probability density function of a discrete random variable and the probability density function of a continuous random variable.
		The difference is that a single value f(x) of the probability density function of a discrete random variable gives a probability, but a single value f(x) of the probability density function of a continuous random variable does NOT give a probability.
	www.es.ucl.ac.uk /undergrad/geomaths/9-pro/pro8.htm (334 words)

	All Elementary Mathematics - Study Guide - Probability - Random variables...
		A variable is called random, if it can receive real values with definite probabilities as a result of experiment.
		The function f (x) is called a density function of continuous random variable.
		The probability of the fact that a random variable X receives a value less than x, is called a distribution function of random variable X and marked as F (x) :
	www.bymath.com /studyguide/prob/sec/prob4.htm (134 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The time between crashes of a computer is represented by the random variable X, whose p.d.f is EMBED Equation.3 for x EMBED Equation.3 0 where x is time in days.
		Let X be a binomial random variable with parameters n=20 and p=0.6.
		The scores X in a Calculus class is a continuous random variable that is uniformly distributed between 75% and 95%.
	math.arizona.edu /~roddier/ind5.doc (398 words)

	Continuous Random Variables & Distributions (Site not responding. Last check: 2007-10-08)
		random variable X is one which can take on any real value in some range of (or anywhere along) the real line
		Unlike with discrete r.v.’s, the measurement scale for a continuous r.v.
		Thus, a p.m.f cannot be defined for a continuous r.v.
	www.pitt.edu /~jrclass/e20/notes/OH13.html (145 words)

	[No title]
		The fundamental difference between the continuous and discrete random variable is that we cannot assign the probability to specific numbers for the case of continuous random variable.
		For example, Q1, Q2, Q3 and various other figures like (10th percentile, etc.) are very important in income distribution (may be more important than the GDP - the average — for some purpose.) In particular, the 50th percentile (Q2) is called the median.
		Variance is the weighted average of (x - ()2 with weight f(x)dx, which is approximately EMBED Equation.DSMT4 .
	www.bus.ucf.edu /kim/eco6416/continuous.doc (1409 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		If you mean to refer to a random variable that has a density function, call it “a random variable that has a density function.”) Having P(X = a) = 0 for all a is necessary, but not sufficient for X to have a density function.
		Suppose X is a random variable, and that its cumulative distribution function F has the following properties: (a) F(x) is continuous for every value of x, and (b) F(x) has a derivative for all x, except possibly for some isolated values.
		Expected values of continuous random variables Let’s use the analogy in the last section to guess a formula for the expected value of a continuous random variable.
	www.chesco.com /~marys/math/M205/notes4.doc (3090 words)

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