Probability

Probability[pred,xdist]

gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution dist.

Probability[pred,xdata]

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,…}dist]

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

Probability[pred,{x1dist1,x2dist2,…}]

gives the probability that an event satisfies pred under the assumption that x1, x2, … are independent and follow the distributions dist1, dist2, ….

Probability[pred1pred2,…]

gives the 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.
  • 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 {v1,v2,…} and multivariate data is given as a list of vectors {{v11,…,v1m},{v21,…,v2m},…}.
  • Probability[pred,{x1dist1,x2dist2}] corresponds to Expectation[Probability[pred,x2dist2],x1dist1] 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$Assumptionsassumptions to make about parameters
    GenerateConditionsFalsewhether to generate conditions on parameters
    MethodAutomaticwhat method to use

Background & Context

Examples

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Basic Examples  (3)

Compute the probability of a simple event:

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Compute the probability of nonlinear and logical combination of inequalities:

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Compute a conditional probability:

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Scope  (29)

Generalizations & Extensions  (3)

Options  (5)

Applications  (50)

Properties & Relations  (11)

Neat Examples  (1)

Introduced in 2010
(8.0)
|
Updated in 2016
(10.4)