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# Topic: Random variable

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 NationMaster - Encyclopedia: Discrete random variable 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. 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. 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. www.nationmaster.com /encyclopedia/Discrete-random-variable   (392 words)

 Random variable - Wikipedia, the free encyclopedia A random variable is a mathematical function that maps statistical events to numbers. 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   (1245 words)

 Random Variables - EXPECTED VALUE OF A RANDOM VARIABLE The mean of a random variable, also known as its expected value, is the weighted average of all the values that a random variable would assume in the long run. The expected value 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 the mean is computed. The expected value of the function g(X) of a discrete random variable X is the mean of another random variable Y which assumes the values of g(X) according to the probability distribution of X. library.thinkquest.org /10030/5rvevoar.htm   (553 words)

 Statistics Glossary - Probability 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; 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)

 Discrete probability distribution - Wikipedia, the free encyclopedia If a random variable is discrete, then the set of all values that it can assume with nonzero probability 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. But there are discrete random variables for which this countable set is dense on the real line. Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf) increases only by jump discontinuities — that is, its cdf increases only where it "jumps" to a higher value, and is constant between those jumps. en.wikipedia.org /wiki/Discrete_random_variable   (372 words)

 Reference.com/Encyclopedia/Random variable In probability theory, a random variable is a quantity whose values are random and to which a probability distribution is assigned. Formally, a random variable is a measurable function from a sample space to the measurable space of possible values of the variable. Associating a cumulative distribution function with a random variable is a generalization of assigning a value to a variable. www.reference.com /browse/wiki/Random_variable   (1111 words)

 Random Variables - EXPECTED VALUE OF A RANDOM VARIABLE The mean of a random variable, also known as its expected value, is the weighted average of all the values that a random variable would assume in the long run. The expected value 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 the mean is computed. The expected value of the function g(X) of a discrete random variable X is the mean of another random variable Y which assumes the values of g(X) according to the probability distribution of X. library.advanced.org /10030/5rvevoar.htm   (553 words)

 Random Variables - VARIANCE OF A RANDOM VARIABLE   (Site not responding. Last check: ) 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)

 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)

 RANDOM RANDOM with no options causes a normal random variable with mean zero and variance one to be generated and stored as a series (under control of the current SMPL). To create a random variable from an empirical distribution function, a series (usually a set of residuals) generated by the distribution function must be supplied. All other random variables are derived from the uniform random variables using the inverse distribution function, which usually involves an asymptotic expansion (see the CDF references). www.tspintl.com /products/tsphelp/random.htm   (1531 words)

 Random variable   (Site not responding. Last check: ) A random variable can be thought of as the result of operating a non-deterministic mechanism or a non-deterministic experiment to generate a random result. In measure-theoretic terms we use the random variable X to "push-forward" the measure P on Ω to a measure d F on R. The probability distribution of random variable is characterised by a small number of parameters also have a practical interpretation. www.freeglossary.com /Random_Variable   (1110 words)

 [No title] Random and Fixed Effects The terms “random” and “fixed” are used in the context of ANOVA and regression models, and refer to a certain type of statistical model. Random effects models are sometimes referred to as “Model II” or “variance component models.” Analyses using both fixed and random effects are called “mixed models.” Fixed and Random Coefficients in Multilevel Regression The random vs. fixed distinction for variables and effects is important in multilevel regression. It is important to distinguish between a variable that is varying and a variable that is random. www.upa.pdx.edu /IOA/newsom/mlrclass/ho_randfixd.doc   (935 words)

 Random Variables A random variable is unknown before the experiment is carried out, but after the experiment is carried out the value of the random variable is always known. Whether or not the shipment is rejected is not a random variable b/c it is not in numerical form. The standard deviation of a random variable indicates the extent of the dispersion or variability among the values that the random variable may assume. www.unc.edu /~knhighto/econ70/lec6/lec6.htm   (777 words)

 [No title] A random variable is not a variable in the same sense the word is used in calculus or algebra: It is something that takes a random value, depending on the outcome of a random experiment. The number of random draws with replacement from a 0-1 box until the first time a ticket labeled "1" is drawn is a random variable with a geometric distribution with parameter p=G/N, where G is the number of tickets labeled "1" in the box and N is the total number of tickets in the box. Even though the random variable X counts "successes" in a fixed number (four) of independent trials, it does not have a binomial probability distribution, because the probability of success is not the same in every trial: It is 1/2 in the trials that involve the coin, and 1/6 in the trials that involve the die. www.stat.berkeley.edu /users/stark/SticiGui/Text/ch12.htm   (5742 words)

 8.1 Random Variables Random variables are mathematical quantities that are used to represent probabilistic uncertainty. The variance or dispersion of a distribution: this indicates the spread of the distribution with respect to the mean value. A lower value of variance indicates that the distribution is concentrated close to the mean value, and a higher value indicates that the distribution is spread out over a wider range of possible values. www.ccl.rutgers.edu /~ssi/thesis/thesis-node52.html   (1074 words)

 math lessons - Random variable 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. 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. www.mathdaily.com /lessons/Random_variable   (1190 words)

 S.O.S. Mathematics CyberBoard :: View topic - A quick question about continuous uniform random variable It is true that for any continuous random variable that the probability of assuming a specific value is zero, so that it doesn't matter whether you include it as part of an inequality or not. We know for a continuous random variable the "probability of a specific point" is zero. For a random variable that is uniform on www.sosmath.com /CBB/viewtopic.php?t=27318&start=0&postdays=0&postorder=asc&highlight=   (717 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. Such a distribution occurs whenever a random variable can be conceptualized as counting the number of "successes" in several independent "trials" of an experiment where the probability of success in each trial is the same. www.math.ohiou.edu /~just/WINTER250/randvarp.htm   (1161 words)

 Random Variables and Statistics X is a finite random variable that can assume the three values: 0, 1, 2, and 3. For a continuous random variable, a mode is a number m such that the probability density function is highest at x = m. The variance and standard deviation of a random variable are the sample variance and sample standard deviation we expect to get if we have a large number of X-scores. www.zweigmedia.com /ThirdEdSite/Summary7.html   (1971 words)

 What is a random variable A random experiment is an experiment whose outcome is unknown before it is performed. A random variable is a mapping from the outcomes of a random experiment to the set of real numbers. In many cases the random variable already comes with a number "attached"; for example when we toss a die the outcome is 1,2,3,4,5, or 6. www.scsu.edu /Psy&Soc/psychology/Geoff/Statisticshandbook2/What_is_a_random_variable.html   (842 words)

 random A standard normal random variable generates sequences of random numbers with mean zero and variance one. The area between the bell shaped curve and the x-axis is equal to one and the area in yellow represents the probability that a value generated from a standard normal random variable falls within the interval [0,1/2]. Random numbers are available for a wide variety of random variables. www.colorado.edu /Economics/courses/Jose/4838/notes/chapter5/simulation/random.htm   (2156 words)

 PlanetMath: symmetric random variable There are many examples of symmetric random variables, and the most common one being the normal random variables centered at 0. Cross-references: identically distributed, independent, normal random variables, density function, continuous at, distribution function, random variable, real, probability space This is version 5 of symmetric random variable, born on 2006-11-22, modified 2006-11-26. planetmath.org /encyclopedia/SymmetricRandomVariable.html   (106 words)

 Math Forum - Ask Dr. Math The traditional symbol for the sample standard deviation is S (lowercase or uppercase; there is a slight difference between the two) and the equivalent Greek letter sigma (which looks like an o with a little tail sticking out from the top) is commonly used to denote the population standard deviation. For example, the expected value of the random variable X, E(X), would be the value we expect this variable to take on average, which is nothing more than the population mean. Sometimes it is possible in advance to know the population variance if we know the population mean and the distribution of the random variable in question (our random variable in our thermometer example was the reading of the thermometer). mathforum.org /library/drmath/view/52723.html   (892 words)

 Random variable - QuickSeek Encyclopedia   (Site not responding. Last check: ) A random variable is a term used in mathematics and statistics. For example, a random variable can be used to describe the process of rolling a fair die and the possible outcomes { 1, 2, 3, 4, 5, 6 }. If a random variable $X: \Omega \to \mathbb\left\{R\right\}$ defined on the probability space $\left(\Omega, P\right)$ is given, we can ask questions like "How likely is it that the value of $X$ is bigger than 2?". randomvariable.quickseek.com   (1262 words)

 Computer Generated Random Numbers A random variable is a function which maps the elements of the sample space S to points on the real number line RR. The random variable function is denoted by a capital X. An actual value a random variable X takes on is denoted by a lowercase x. The first random number is used to pick an element from the array of random numbers, and the second random number is used to replace the number chosen. world.std.com /~franl/crypto/random-numbers.html   (10155 words)

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