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# Topic: Discrete random variable

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 Continuous random variable - Wikipédia 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. su.wikipedia.org /wiki/Continuous_random_variable   (196 words)

 Discrete random variable - Wikipedia, the free encyclopedia In mathematics, a random variable is discrete if its probability distribution is discrete; a discrete probability distribution is one that is fully characterized by a probability mass function. The Poisson distribution, the Bernoulli distribution, the binomial distribution, the geometric distribution, and the negative binomial distribution are among the most well-known discrete probability distributions. If a random variable is discrete then the set of all possible values that it can assume is finite or countably infinite, because the sum of uncountably many positive real numbers (which is the smallest upper bound of the set of all finite partial sums) always diverges to infinity. en.wikipedia.org /wiki/Discrete_random_variable   (159 words)

 [No title]   (Site not responding. Last check: 2007-11-06) Mathematically, a random variable is defined as a measurable function from a probability space to some measurable space. In measure-theoretic terms, we use the random variable X to "push-forward" the measure P on Ω to a measure dF on R. The probability distribution of random variable is often characterised by a small number of parameters, which also have a practical interpretation. www.informationgenius.com /encyclopedia/r/ra/random_variable_1.html   (597 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. 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. 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, or a process where components from a production line are tested, in turn, until the first defective item is found. www.stats.gla.ac.uk /steps/glossary/probability_distributions.html   (2101 words)

 Probability density function of a Random Variable   (Site not responding. Last check: 2007-11-06) A discrete random variable is a number corresponds to an outcome of a non predictable event. Discrete implies that the values of the variable are either either limited to whole numbers or are from a finite set of values. Examples of random variables are: the number of thunderstorms in an area in a given season, the number of aces in a poker hand, or the payoff of a lottery ticket. www.unca.edu /math/OnLine/Stat220/Lesson/L_MS_Dpdf.html   (318 words)

 Probability distribution - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-11-06) A distribution is called discrete if its cumulative distribution function consists of a sequence of finite jumps, which means that it belongs to a discrete random variable X: a variable which can only attain values from a certain finite or countable set. That discrete distributions do not admit such a density is unsurprising, but there are continuous distributions like the devil's staircase that also do not admit a density. In digital computers, pseudo-random number generators are used to produced a statistically random discrete uniform distribution. encyclopedia.worldsearch.com /probability_distribution.htm   (1176 words)

 PlanetMath: uniform (discrete) random variable is a uniform (discrete) random variable with parameter "uniform (discrete) random variable" is owned by Riemann. This is version 2 of uniform (discrete) random variable, born on 2001-10-26, modified 2002-02-17. planetmath.org /encyclopedia/UniformDiscreteRandomVariable.html   (60 words)

 [No title]   (Site not responding. Last check: 2007-11-06) For a discrete random variable (one that has a countable number of possible values) the expected value is the weighted average of its possible values, where the weight assigned to each possible value is the chance that the random variable takes that value. In regression, the independent variable is the one that is supposed to explain the other; the term is a synonym for "explanatory variable." Usually, one regresses the "dependent variable" on the "independent vaiable." There is not always a clear choice of the independent variable. In linear regression of a variable plotted on the vertical axis onto a variable plotted on the horizontal axis, a residual is the "vertical" distance from a datum to the line. www.maths.qmw.ac.uk /~mjt/stat-inf/general/gloss.html   (3608 words)

 Probability distribution The discrete uniform distribution, where all elements of a finite set are equally likely. The Boltzmann distribution, a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system in thermal equilibrium. The F-distribution, which is the distribution of the ratio of two normally distributed random variables, used in the analysis of variance. www.nebulasearch.com /encyclopedia/article/Probability_distribution.html   (1151 words)

 Discrete Random Variables   (Site not responding. Last check: 2007-11-06) A random variable that can take on at most a countable number of possible values, like the dice throwing example on the previous page, is said to be a Discrete Random Variable. For discrete random variable X, the probability mass function p(a) of X is defined by the following function. A random variable X is defined as a Bernoulli random variable if its probability mass function is given by these equations. cne.gmu.edu /modules/dau/prob/randomvarsdrv_bdy   (213 words)

 * Discrete random variable - (Business): Definition   (Site not responding. Last check: 2007-11-06) A random variable that can take only a certain specified set of individual possible values-for example, the positive integers 1, 2, 3,... Definition: A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,... Discrete random variable A random variable that can take only a certain specified set of individual possible values-for example, the positive integers 1, 2, 3,... www.mimihu.com /business/discrete_random_variable.html   (124 words)

 Statistics Glossary - Probability Discrete case : When a die is thrown, each of the possible faces 1,2,3,4,5,6 - the xi's - has a probability of 1/6 - the p(xi)'s - of showing. 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. www.cas.lancs.ac.uk /glossary_v1.1/prob.html   (3540 words)

 Random variable   (Site not responding. Last check: 2007-11-06) 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. Two random variables can be equal, equal almost surely, equal in mean, or equal in distribution. To be equal in distribution, random variables need not be defined on the same probability space, but without loss of generality they can be made into independent random variables on the same probability space. www.sciencedaily.com /encyclopedia/random_variable_1   (902 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)

 STAT 301: ELEMENTARY STATISTICS   (Site not responding. Last check: 2007-11-06) A random variable is a quantitative variable whose value depends on chance. The uppercase X is the random variable while lowercase x designates a particular value taken by X. So the probability that. The probability distribution is a listing of the possible values and corresponding probabilities of a discrete variable, or a formula for the probabilities. www.math.niu.edu /~hzhang/stat301/Chap05/05.htm   (306 words)

 GLOSSARY The cumulative distribution function of a random variable X, F(x), is the probability that X is less than or equal to x. The value of a statistic that is a random variable used as an estimator of the parameter. A random variable that can be calculated from sample data which is used to give information about an unknown quantity in the population. www.maths.qut.edu.au /MAB893/glossa_n.htm   (1546 words)

 AMS 311 Definition The expected value of a discrete random variable X with the probability function p(x) and set of possible values A (that is, those values x with p(x)>0) is defined by 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. Let X be a discrete random variable with the set of possible values A, and mean :. www.ams.sunysb.edu /~dorothy/handout11.html   (220 words)

 Section 2 - Random variables A random variable is a variable that has a single numeric value for each outcome of an experiment. Note the values for the random variable are given in the left column and the probability of each outcome is given in the right column. The expected value (or expectation) of a discrete random variable is denoted E, and it represents the average value of all outcome. wind.cc.whecn.edu /~pwildman/statnew/new_page_1.htm   (922 words)

 5.3 Numerical characteristics of a discrete random variable   (Site not responding. Last check: 2007-11-06) 5.3 Numerical characteristics of a discrete random variable Since a probability distribution for a random variable x is a model for a population relative frequency distribution, we can describe it with numerical descriptive measures, such as its mean and standard deviation, and we can use Chebyshev theorem to identify improbable values of x. Let x be a discrete random variable with probability distribution p(x) and let g(x) be a function of x. www.netnam.vn /unescocourse/statistics/53.htm   (329 words)

 3. Random Variables & Probability Distributions A discrete random variable, x, occurs with probability f(x) and is an element of the finite or countably infinite set of all possible events X. A continuous random variable is defined for some interval on the line of real numbers; but the probability that a continuous random variable, x, takes on any specified real value in the interval is equal to zero. The normal, or Gaussian, distribution is widely applicable as a probability model for continuous random variables that may be thought of as resulting from the sum of a large number of small effects. mcardle.oncology.wisc.edu /mstat/Mhelp/StatNotes-3.html   (4656 words)

 Random variable - Wikipedia We can think of a random variable as a numeric result of operating a non-deterministic mechanism. We can always specify a random variable by specifying its cumulative distribution function because two random variables with identical cdf's are isomorphic. Similarly, while the CDF for a random variable whose range is more than one-dimensional can be defined, it is much more difficult to deal with. nostalgia.wikipedia.org /wiki/Random_variable   (201 words)

 Discrete Random Variables   (Site not responding. Last check: 2007-11-06) Thus the value taken by the random variable will not be known until the experiment has been carried out. random variables can only take a finite or countable number of values, and have a positive probability of taking each one; typically these are integer-valued quantities obtained by counting. The graph of the distribution function of a discrete random variable is flat, except for some upward jumps: the height of the jump at x is p www.student.city.ac.uk /~sc397/courses/1pr/1pr9893.html   (786 words)

 St@tmaster - Keywords   (Site not responding. Last check: 2007-11-06) A random variable is a function that assigns a number to an event in a given sample space. Throw a die and let the random variable X be the face value, while the random variable Y is the number of throws, until you get a 6. These 4 random variables are continuous, while the former are discrete. statmaster.sdu.dk /keywords/r/randomvar.html   (167 words)

 Random variable Details, Meaning Random variable Article and Explanation Guide For example, rolling a dice and recording the outcome yields a random variable with range { 1, 2, 3, 4, 5, 6 }. If a random variable defined on the probability space is given, we can ask questions like "How likely is it that the value of is bigger than 2?". There are several different senses in which random variables can be considered to be equivalent. www.e-paranoids.com /r/ra/random_variable_1.html   (863 words)

 Random Variables and Probability Distributions   (Site not responding. Last check: 2007-11-06) gives the variance of the observed values of x over the long run, and so, together with its square root (which would be the standard deviation of the observed values of x over the long run) is a measure of how much spread there is in the observed values of x. The possible values of a discrete random variable form a set of specific, isolated values, to each of which can be assigned a probability. Continuous random variables have mean values, variances, and other expected values in the same way that discrete random variables do, except that now, the summation is replaced by an integral involving the probability density function. www.math.bcit.ca /faculty/david_sabo/apples/math2441/section5/calcprob3/calcprob3.htm   (3034 words)

 Common Discrete Probability Functions A discrete random variable is used to model a random outcome with a finite or countable number of possible outcomes. That is, a discrete random variable is one that may take on only a countable number of distinct values. The cumulative distribution function of a random variable is a function giving the probability that the random variable X is less than or equal to x, for every value x, i.e. home.ubalt.edu /ntsbarsh/Business-stat/otherapplets/DiscreteProb.htm   (368 words)

 Need help for stats. (Discrete random variable)!   (Site not responding. Last check: 2007-11-06) The random varibale X represents the amount, in pence, that he puts in the box. Variance is never negative (because it is the expectation of (X - E(X))^2, and that thing is at least 0). Z usually represents a normal random variable with mean 0 and variance 1 - called a "standard" normal random variable. www.thestudentroom.co.uk /t72040.html   (1046 words)

 Discrete random variable A random variable is discrete if the set of all possible values that it can assume is finite or countably infinite. The probability that a discrete random variable will take any particular value is given by the probability mass function. The text of this article is licensed under the GFDL. www.ebroadcast.com.au /lookup/encyclopedia/di/Discrete_random_variable.html   (60 words)

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