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description=Probability[pred, x \[Distributed] dist] gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution dist. Probability[pred, x \[Distributed] data] gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution given by data. Probability[pred, x1, x2, ... \[Distributed] dist] gives the probability that an event satisfies pred under the assumption that x1, x2, ... follows the multivariate distribution dist. Probability[pred, x1 \[Distributed] dist1, x2 \[Distributed] dist2, ... ] gives the probability that an event satisfies pred under the assumption that x1, x2, ... are independent and follow the distributions dist1, dist2, .... Probability[pred1 \[Conditioned] pred2, ...] gives the conditional probability of pred1 given pred2.;

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Text of the page (random words):
ram consulting data science finance business artificial intelligence data science healthcare real estate engineering civil engineering automotive engineering sustainable energy science technology agtech biosciences environmental science food science quantum computation social and behavioral sciences more wolfram solutions technology for education research universities colleges teaching universities high schools resources for students education initiatives next gen edtech computer based math more solutions for education contact us learning support get started wolfram language introduction fast intro for programmers fast intro for math students wolfram language documentation grow your skills wolfram u courses in computing science life and more community learn solve problems and share ideas blog news views and insights from wolfram resources for software developers tech support contact us support faqs more learning highlighted core areas demonstrations youtube daily study groups wolfram schools and programs books support faqs contact us company about wolfram career center all sites resources connect follow contact us work with us student ambassador initiative wolfram for startups student opportunities jobs using wolfram language educational programs for adults summer school winter school educational programs for youth middle school camp high school research program computational adventures read stephen wolfram s writings wolfram blog wolfram tech books wolfram media complex systems educational resources wolfram mathworld wolfram in stem wolfram challenges wolfram problem generator wolfram initiatives wolfram science wolfram foundation history of mathematics project events stephen wolfram livestreams online in person events contact us connect follow for ais wolfram cloud your account user portal enable javascript to interact with content and submit forms on wolfram websites learn how wolfram language system documentation center close probability see also nprobability distributed conditioned expectation nexpectation cdf pdf survivalfunction probabilitydistribution sum integrate regionplot related guides random variables probability statistics random processes actuarial computation finite mathematics scientific models solvers over regions statistical data analysis reliability random graphs descriptive statistics probability statistics with quantities see also nprobability distributed conditioned expectation nexpectation cdf pdf survivalfunction probabilitydistribution sum integrate regionplot related guides random variables probability statistics random processes actuarial computation finite mathematics scientific models solvers over regions statistical data analysis reliability random graphs descriptive statistics probability statistics with quantities probability pred x dist gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution dist probability pred x data gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution given by data probability pred x 1 x 2 dist gives the probability that an event satisfies pred under the assumption that x 1 x 2 follows the multivariate distribution dist probability pred x 1 dist 1 x 2 dist 2 gives the probability that an event satisfies pred under the assumption that x 1 x 2 are independent and follow the distributions dist 1 dist 2 probability pred 1 pred 2 gives the conditional probability of pred 1 given pred 2 details and options background context examples basic examples scope basic uses quantity uses parametric distributions nonparametric distributions derived distributions generalizations extensions options assumptions method applications random experiments sports and games actuarial science weather traffic reliability communication quality probability visualizations other applications elections boy or girl theoretical versus sample probabilities triangle construction regions properties relations neat examples see also related guides history cite this page built in symbol see also nprobability distributed conditioned expectation nexpectation cdf pdf survivalfunction probabilitydistribution sum integrate regionplot related guides random variables probability statistics random processes actuarial computation finite mathematics scientific models solvers over regions statistical data analysis reliability random graphs descriptive statistics probability statistics with quantities see also nprobability distributed conditioned expectation nexpectation cdf pdf survivalfunction probabilitydistribution sum integrate regionplot related guides random variables probability statistics random processes actuarial computation finite mathematics scientific models solvers over regions statistical data analysis reliability random graphs descriptive statistics probability statistics with quantities probability probability pred x dist gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution dist probability pred x data gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution given by data probability pred x 1 x 2 dist gives the probability that an event satisfies pred under the assumption that x 1 x 2 follows the multivariate distribution dist probability pred x 1 dist 1 x 2 dist 2 gives the probability that an event satisfies pred under the assumption that x 1 x 2 are independent and follow the distributions dist 1 dist 2 probability pred 1 pred 2 gives the conditional probability of pred 1 given pred 2 details and options x dist can be entered as x dist dist or x distributed dist pred 1 pred 2 can be entered as pred 1 cond pred 2 or pred 1 conditioned pred 2 for a continuous distribution dist the probability of pred is given by boole pred f x x where f x is the probability density function of dist and the integral is taken over the domain of dist for a discrete distribution dist the probability of pred is given by boole pred f x where f x is the probability density function of dist and the summation is taken over the domain of dist for a dataset data the probability of pred is given by sum boole pred x data length data univariate data is given as a list of values v 1 v 2 and multivariate data is given as a list of vectors v 11 v 1 m v 21 v 2 m probability pred x 1 dist 1 x 2 dist 2 corresponds to expectation probability pred x 2 dist 2 x 1 dist 1 so that the last variable is summed or integrated first n probability calls nprobability for probabilities that cannot be evaluated symbolically the following options can be given assumptions assumptions assumptions to make about parameters generateconditions false whether to generate conditions on parameters method automatic what method to use background context probability pred x represents the probability for an event that satisfies a predicate pred under the assumption that the chosen random variable x follows an indicated probability distribution i e is a discrete or continuous distribution such as normaldistribution binomialdistribution chisquaredistribution etc or is taken from a given dataset i e defines a dataset and where is a shorthand for distributed the output of probability is either a number where the probability of an impossible event is 0 while the probability for a certain event is 1 or a symbolic expression involving the input parameters probability also works with multivariate distributions with nonparametric distributions such as empiricaldistribution histogramdistribution and kernelmixturedistribution and with derived distributions such as transformeddistribution and productdistribution in addition probability may be applied to random processes including those defined by continuousmarkovprocess discretemarkovprocess wienerprocess and poissonprocess the predicate pred may include both linear and nonlinear inequalities as well as logical combinations of inequalities probability can compute conditional probabilities using a predicate of the form pred 1 pred 2 where is a shorthand for conditioned a number of options may be passed to probability including assumptions generateconditions and method the output provided by probability is calculated using exact methods such as symbolic integration and summation corresponding results involving numerical methods can be obtained via nprobability several wolfram language functions including pdf cdf and survivalfunction return results that are equivalent to those obtainable using probability with particular predicate structures in addition results obtained by probability may be obtained by expectation by pairing expectation with a boole construct for example expectation boole 1 x 3 x normaldistribution is equivalent to probability 1 x 3 x normaldistribution probability can be used to exactly solve many problems in probability for example the probability that a toss of two dice will yield a sum of 3 or 4 is given by probability 3 x y 4 x y discreteuniformdistribution 1 6 1 6 while the chances that a triple of uniformly distributed random variables satisfying will yield a polynomial with real roots can be computed using probability b 2 4 a c 0 a b c uniformdistribution table 0 1 3 examples open all close all basic examples 3 compute the probability of a simple event wolfram language code probability x 3 x normaldistribution wolfram language code probability x 3 x poissondistribution μ wolfram language code probability x 1 2 y 1 3 x y dirichletdistribution 1 4 5 wolfram language code probability x 2 y 3 x y multivariatepoissondistribution 1 2 3 compute the probability of nonlinear and logical combination of inequalities wolfram language code probability x 1 2 3x x normaldistribution wolfram language code probability x 2 3 abs x 1 x 1 2 3 wolfram language code probability x 2 3 abs x 1 x exponentialdistribution λ wolfram language code probability x 2 y 2 1 4 x y 6 7 x y dirichletdistribution 2 3 4 wolfram language code plot3d pdf dirichletdistribution 2 3 4 x y x 0 3 5 y 0 3 5 regionfunction function x y z x 2 y 2 1 4 x y 6 7 mesh none plotstyle opacity 0 7 filling bottom compute a conditional probability wolfram language code probability x 2 1 x 1 2 x laplacedistribution 0 1 2 wolfram language code probability x y 2 z 2 3 10 x 1 7 y 1 4 x y z dirichletdistribution 1 3 4 7 scope 30 basic uses 9 compute the probability of an event in a continuous univariate distribution wolfram language code probability 3 x 5 x normaldistribution discrete univariate distribution wolfram language code probability 1 x 7 x poissondistribution 1 continuous multivariate distribution wolfram language code probability 0 x 5 2 1 2 y 8 x y dirichletdistribution 1 2 3 discrete multivariate distribution wolfram language code probability 1 x 5 2 5 y 8 x y z multinomialdistribution 10 1 3 1 2 1 6 find the probability of an event in a distribution specified by a list wolfram language code r randomvariate normaldistribution 1000 wolfram language code probability x 2 3x 11 x r compute the probability using independently distributed random variables wolfram language code probability 1 x 5 3 y 8 x exponentialdistribution 1 y normaldistribution wolfram language code n find the conditional probability with general nonzero probability conditioning wolfram language code probability x 2 1 2 x 2 5 x exponentialdistribution λ wolfram language code plot λ 0 5 discrete univariate distribution wolfram language code probability x 2 12 x 2 x poissondistribution λ wolfram language code plot λ 0 10 multivariate continuous distribution wolfram language code probability x y 7 10 y 1 3 x y dirichletdistribution 1 3 4 multivariate discrete distribution wolfram language code probability x y 5 z 2 x y z multinomialdistribution 10 1 3 1 2 1 6 compute the conditional probability with a zero probability conditioning event wolfram language code probability x y 2 3 10 x 1 7 x y dirichletdistribution 1 3 4 apply n probability to invoke nprobability if symbolic evaluation fails wolfram language code f x_ numericq x 3 wolfram language code probability f x 1 x normaldistribution wolfram language code n wolfram language code nprobability f x 1 x normaldistribution with no assumptions conditions are generated wolfram language code probability x a x uniformdistribution 2 8 with assumptions a result valid under the given assumptions is returned wolfram language code probability x a x uniformdistribution 2 8 assumptions 5 a 7 wolfram language code assuming 5 a 7 probability x a x uniformdistribution 2 8 use nonlinear predicates and arbitrary logical combinations wolfram language code probability x 2 5 2x 3 5 x 3 x 11 x exponentialdistribution 2 calculate the probability of an event for a time slice of a poisson process wolfram language code probability x t 2 x t 34 x poissonprocess μ quantity uses 3 probability of events specified using quantity wolfram language code probability quantity x meters quantity 3 feet x lognormaldistribution 2 3 probability involving quantitydistribution wolfram language code probability x quantity 3 meters x quantitydistribution weibulldistribution 2 3 yards conditional probability specified using quantity wolfram language code probability x quantity y pounds x quantity 3 grams x quantitydistribution exponentialdistribution 3 grams y gammadistribution 2 3 parametric distributions 5 compute probabilities for univariate continuous distributions wolfram language code probability x 1 2 x betadistribution α β wolfram language code probability 3 x 2 7 x uniformdistribution 2 11 wolfram language code probability x 3 2 5 x normaldistribution 0 1 wolfram language code probability e x 3x x chisquaredistribution ν compute probabilities for univariate discrete distributions wolfram language code probability 2 x 9 x binomialdistribution 10 p wolfram language code probability x 10 x discreteuniformdistribution min max wolfram language code probability x 3 12 x zipfdistribution ρ wolfram language code probability e 2x 3 x poissondistribution λ probabilities for multivariate continuous distributions wolfram language code probability x y 2 7 x uniformdistribution 0 1 y laplacedistribution 0 1 wolfram language code probability x 3y 1 x normaldistribution 0 1 y exponentialdistribution m wolfram language code probability 1 3 x 1 2 1 7 y 11 13 x y z dirichletdistribution 2 3 4 7 probabilities for multivariate discrete distributions wolfram language code probability x y 2 6 x y productdistribution discreteuniformdistribution 2 5 bernoullidistribution p wolfram language code probability x y 4 x zipfdistribution 3 y poissondistribution λ wolfram language code probability 2 x 8 5 y 8 z 3 x y z discreteuniformdistribution 2 12 4 11 2 7 compare two normally distributed random variables wolfram language code probability x y x normaldistribution μ1 σ1 y normaldistribut...