NProbability

NProbability[pred,xdist]
gives the numerical probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution dist.

NProbability[pred,{x1,x2,}dist]
gives the numerical probability that an event satisfies pred under the assumption that {x1,x2,} follows the multivariate distribution dist.

NProbability[pred,{x1dist1,x2dist2,}]
gives the numerical probability that an event satisfies pred under the assumption that x1, x2, are independent and follow the distributions dist1, dist2, .

NProbability[pred1pred2,]
gives the numerical conditional probability of pred1 given pred2.

Details and OptionsDetails and Options

  • xdist can be entered as x EscdistEsc dist or x[Distributed]dist.
  • pred1pred2 can be entered as pred1 EsccondEsc pred2 or pred1[Conditioned]pred2.
  • NProbability works like Probability except numerical summation and integration methods are used.
  • 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.
  • NProbability[pred,{x1dist1,x2dist2}] corresponds to NExpectation[NProbability[pred,x2dist2],x1dist1] so that the last variable is summed or integrated first.
  • N[Probability[]] calls NProbability for probabilities that cannot be done symbolically.
  • The following options can be given:
  • AccuracyGoaldigits of absolute accuracy sought
    PrecisionGoalAutomaticdigits of precision sought
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
    MethodAutomaticwhat method to use

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Compute the probability of a simple event:

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Compute the probability of a nonlinear and logical combination of inequalities:

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Compute a conditional probability:

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Introduced in 2010
(8.0)