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# Topic: Bernoulli distribution

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 math lessons - Probability distribution A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space. The rectangular distribution is a uniform distribution on [-1/2,1/2]. The triangular distribution on [a, b], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions). www.mathdaily.com /lessons/Probability_distribution   (1245 words)

 PlanetMath: binomial distribution   (Site not responding. Last check: 2007-11-07) We will use the moment generating function to calculate the mean and variance for the distribution. Cross-references: normal distribution, Poisson distribution, binomial coefficients, derivative, function, variance, mean, moment generating function, expansion, binomial, calculate, probability function, distribution function, outcomes This is version 12 of binomial distribution, born on 2002-09-13, modified 2004-06-28. planetmath.org /encyclopedia/BinomialRandomVariable.html   (167 words)

 Binomial distribution - Wikipedia, the free encyclopedia In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. The binomial distribution is the basis for the popular binomial test of statistical significance. This approximation is a huge time-saver; historically, it was the first use of the normal distribution, introduced in Abraham de Moivre's book The Doctrine of Chances in 1733. en.wikipedia.org /wiki/Binomial_distribution   (739 words)

 Encyclopedia: Bernoulli distribution   (Site not responding. Last check: 2007-11-07) In probability theory, the cumulative distribution function (abbreviated cdf) completely describes the probability distribution of a real-valued random variable, X. For every real number x, the cdf is given by where the right-hand side represents the probability that the variable X takes on a value less than or... The probability mass function f of this distribution is In probability theory, a probability mass function (abbreviated pmf) gives the probability that a discrete random variable is exactly equal to some value. The expected value of a Bernoulli random variable X is EX = p, and its variance is In probability (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). www.nationmaster.com /encyclopedia/Bernoulli-distribution   (869 words)

 Distribution Fitting To determine this underlying distribution, it is common to fit the observed distribution to a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution (i.e., a Chi-square goodness of fit test). The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution. The logistic distribution is used to model binary responses (e.g., Gender) and is commonly used in logistic regression. www.statsoftinc.com /textbook/stdisfit.html   (1769 words)

 Bernoulli Distribution A Bernoulli random number is always either a 0 or 1 with the specified probability of being a 1. Bernoulli random numbers are useful in conditional statements using the IF primitive that are designed to model cases where an event either occurs or does not. The Bernoulli distribution is a special application of the Binomial distribution random number brand where the number of trials is set to one. www.vanguardsw.com /dphelp4/dph00127.htm   (97 words)

 Stat. Distributions   (Site not responding. Last check: 2007-11-07) Beta Distribution: A distribution that is useful for random variables constrained to lie between 0 and 1. Logistic Distribution: A distribution useful for random variables that are not constrained to be greater than or equal to 0. Student's t Distribution: A distribution useful in forming confidence intervals for the mean when the variance is unknown, testing to determine if two sample means are significantly different, or testing to determine the significance of coefficients in a regression. www.cise.ufl.edu /~apol/services/distributions.htm   (1086 words)

 Functions and CALL Routines : CDF The CDF function for the Bernoulli distribution returns the probability that an observation from a Bernoulli distribution, with probability of success equal to p, is less than or equal to x. The CDF function for the binomial distribution returns the probability that an observation from a binomial distribution, with parameters p and n, is less than or equal to m. The CDF function for the F distribution returns the probability that an observation from an F distribution, with ndf numerator degrees of freedom, ddf denominator degrees of freedom, and noncentrality parameter nc, is less than or equal to x. www.asu.edu /sas/sasdoc/sashtml/lgref/z0208980.htm   (1101 words)

 Boost Random Number Library Distributions   (Site not responding. Last check: 2007-11-07) In addition to the random number generators, this library provides distribution functions which map one distribution (often a uniform distribution provided by some generator) to another. The distribution functions no longer satisfy the input iterator requirements (std:24.1.1 [lib.input.iterators]), because this is redundant given the Generator interface and imposes a run-time overhead on all users. Such a distribution produces random numbers x > 0 distributed with probability density function p(x) = lambda * exp(-lambda * x), where lambda is the parameter of the distribution. www.boost.org /libs/random/random-distributions.html   (1426 words)

 Probability distribution Article, Probabilitydistribution Information   (Site not responding. Last check: 2007-11-07) The triangular distribution on [a,b], a special case of which is the distribution of the sum of two uniformly distributed random variables (theconvolution of two uniform distributions). The Weibull distribution, of which the exponentialdistribution is a special case, is used to model the lifetime of technical devices. The F-distribution, which is the distribution of the ratio of twonormally distributed random variables, used in the analysis ofvariance. www.anoca.org /random/distributions/probability_distribution.html   (970 words)

 Bernoulli distribution -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07) The (The sum of the values of a random variable divided by the number of values) expected value of a Bernoulli random variable is, and its (The second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value) variance is The Bernoulli distribution is a member of the (Click link for more info and facts about exponential family) exponential family. is a (A theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success) binomial distribution if where is a Bernoulli distribution. www.absoluteastronomy.com /encyclopedia/b/be/bernoulli_distribution.htm   (153 words)

 Discrete Distributions A family of distributions is a set of distributions which all have something in common, usually a similar set of possible values or a similar form for the probabilities. For example, in describing the hypergeometric distribution we emphasized a hypergeometric setting was not a binomial experiment by noting that in a class of 10 women and 30 men, the probability of choosing a man at random was 30/40. The fraction M/N is the proportion of ones in the population, similar to the population proportion p in the Binomial distribution. www.ms.uky.edu /~viele/sta281s99/discdist/discdist.html   (6285 words)

 bernoulli distribution   (Site not responding. Last check: 2007-11-07) Distribution is one of the four aspects of marketing. Bernoulli Distribution A Bernoulli random number is always either a 0 or 1 with the specified probability of being a 1. Bernoulli Distribution An experiment of a particularly simple type is on which there are only two possible outcomes, such as head or tail, success or... www.distribution-logistics.info-a1.com /distributionlogistics/1/bernoulli-distribution.html   (220 words)

 Probability Distributions The distribution of the arrow impacts on the wall is a Cauchy distribution. The Cauchy distribution is (together with the gaussian distribution) a member of the family of "stable distributions" (also called "Levy distributions" or "Levy-stable distributions"): this means that a sum of Cauchy variables is still a Cauchy varible. This is a multidimensionnal generalization of the beta distribution, extensively used in bayesian modelling: the Beta distribution can be used to model the distribution of the p paremeter of a binomial random variable; similarly, the Dirichlet distribution can be used to model the distribution of the probabilities used as parameters of a multinomial distribution. zoonek2.free.fr /UNIX/48_R/07.html   (4940 words)

 [No title]   (Site not responding. Last check: 2007-11-07) The Pascal Distribution is related to the Geometric Distribution in the sense that we wait for the r In some cases, the distribution in question is difficult to calculate whereas we can use another distribution to approximate it. Hypergeometric à Binomial (the Binomial distribution is used to approximate the Hypergeometric one). www.aui.ma /personal/~F.Chaatit/Chapter6.htm   (664 words)

 Stat Lab 4   (Site not responding. Last check: 2007-11-07) For the Cauchy Distribution, the data doesn't follow the requirements for the CLT, so therefore the plot results in an S-curve. In a Bernoulli Distribution Model, two options of "success" and "failure" can occur, with a defineable ratio of successes. According to the Central Limit Theorem, the sample mean from any population will have an approximately normal distribution if the number of observations is large enough and the data has a finite varience. www.kluge.net /~mrv/class/lab4.html   (465 words)

 Introduction As we noted earlier, the most obvious example of Bernoulli trials is coin tossing, where success means heads and failure means tails. In a sense, the most general example of Bernoulli trials occurs when an experiment is replicated. Bernoulli trials are also formed when we sample from a dichotomous population. www.ds.unifi.it /VL/VL_EN/bernoulli/bernoulli1.html   (997 words)

 [No title] Bernoulli Distribution Definition: A random variable X is defined to have a Bernoulli distribution, denoted by X~Be(p), if the pmf of X is given by pX(x) = px(1-p)1-xI{0,1}(x) where the parameter p satisfies 0 Thus, the Binomial distribution is used in modeling the number of successes in a random sample of size n when the sample size is small relative to the size of the population even if sampling is done without replacement. An “old” functioning component has the same lifetime distribution as a “new” functioning component or that the component is not subject to fatigue or to wear. www.upd.edu.ph /~stat/faculty/tgc/Stat121Ch_3.doc   (3310 words)

 Estimating Proportions The distribution of X is known as the Bernoulli distribution with parameter p. The problem of estimating the unknown parameter p in a Bernoulli distribution is important enough to warrant its own section. Show that the variance of the Bernoulli distribution is maximized when p = 1/2 and thus the maximum variance is 1/4. www.fmi.uni-sofia.bg /vesta/Virtual_Labs/interval/interval4.html   (996 words)

 Random Variables and Statistics The empirical probability distribution is given by counting the number of combinations that give 0, 1, 2, or 3 heads. A finite uniform distribution is one in which all values of X are equally likely. For a calculus-based discussion of this and other distributions (the uniform, exponential, and beta distributions) go to the on-line section on probability density functions. www.zweigmedia.com /ThirdEdSite/Summary7.html   (1971 words)

 Bernoulli Distribution   (Site not responding. Last check: 2007-11-07) A theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success. A discrete frequency distribution which, when a chance event has only two possible outcomes, often termed "success" and "failure", each with fixed probabilities of occurring, gives the probabilities of the number of successes in a given number of independent trials of the event. distribuzione di Bernoulli (binomial distribution), distribuzione binomiale (binomial distribution). www.websters-online-dictionary.org /definition/Bernoulli+Distribution   (361 words)

 [No title] This Bernoulli distribution concerns 60 trials of the random process o f throwing a fair die and considering the outcome \lquote obtaining a 4\rquote. \par }\pard\plain \s1\ql \li0\ri0\nowidctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\faauto\outlinelevel0\rin0\lin0\itap0 \fs44\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Bernoulli Distributions \par {\pntext\pard\plain\s2 \f28\fs22 \loch\af28\dbch\af0\hich\f28 \'6e\tab}}\pard\plain \s2\ql \fi-270\li270\ri0\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls1\pnrnot0\pnf28\pnfs22 {\pntxtb n}}\faauto\ls1\outlinelevel1\rin0\lin270\itap0 \fs32\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Given a Bernoulli distribution, the }{\b mean }{of that Bernoulli distribution is number of occurrences of the outcome in question that we expect. }{\super \par }\pard\plain \s1\ql \li0\ri0\nowidctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\faauto\outlinelevel0\rin0\lin0\itap0 \fs44\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Calculating Bernoulli Distributions \par {\pntext\pard\plain\s2 \f28\fs22 \loch\af28\dbch\af0\hich\f28 \'6e\tab}}\pard\plain \s2\ql \fi-270\li270\ri0\nowidctlpar{\*\pn \pnlvlblt\ilvl0\ls1\pnrnot0\pnf28\pnfs22 {\pntxtb n}}\faauto\ls1\outlinelevel1\rin0\lin270\itap0 \fs32\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {This independence from the specific trial(s) in which one actually obtains the sort-after outcome is a general feature of Bernoulli distributions related to the fact that each trial is independent of the others. people.cohums.ohio-state.edu /cole253/153Lec13.rtf   (2738 words)

 Lab 4.1: Glossary   (Site not responding. Last check: 2007-11-07) Bernoulli trial: An occurrence in which exactly one of two possible outcomes can occur. Bernoulli distribution model: Also called simply a Bernoulli distribution, a Bernoulli distribution model describes the pattern of variation of a Bernoulli random variable. The Bernoulli distribution model is characterized by the parameter p in the Bernoulli trial. www.math.wpi.edu /Course_Materials/SAS/lablets/Lab4_1/glossary.html   (142 words)

 Bernoulli Distribution   (Site not responding. Last check: 2007-11-07) In mathematical analysis, distributions (alsoknown as generalized functions) are objects which generalize functions and probabilitydistributions. They extend the concept of derivative to all continuous functions and beyond and are used to formulate generalized solutions of partial differential equations. Sometimes, people talk of a " probability distribution" whenthey just mean "probability measure ", especially ifit is obtained by taking the product of the Lebesgue measure by apositive, real-valued measurable function of integral equal to 1. www.daikaiju.com /edge/22600-bernoulli%20distribution.html   (310 words)

 Bernoulli distribution - Definition up Erdmond.Com   (Site not responding. Last check: 2007-11-07) The probability_mass_function ''f'' of this distribution is : f(x) = p^x(1-p)^{1-x} = \left\{\begin{matrix} p & \mbox {if }x=1, \\ q & \mbox {if }x=0, \\ 0 & \mbox {otherwise.}\end{matrix}\right. The expected_value of a Bernoulli random variable is ''p'', and its variance is ''pq'' = ''p''(1 − ''p''). The Bernoulli distribution is a member of the exponential_family. www.erdmond.com /Bernoulli_distribution.html   (139 words)

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