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 Options

  • xdist can be entered as x dist dist or x[Distributed]dist.
  • pred1pred2 can be entered as pred1 cond 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

Examples

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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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Scope  (27)

Generalizations & Extensions  (2)

Options  (6)

Applications  (26)

Properties & Relations  (11)

Possible Issues  (1)

See Also

Probability  Distributed  Conditioned  Expectation  NExpectation  CDF  PDF  SurvivalFunction  NSum  NIntegrate

Introduced in 2010
(8.0)