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 follows the multivariate distribution dist.

Probability[pred,{x1dist1,x2dist2,}]
gives the probability that an event satisfies pred under the assumption that , , are independent and follow the distributions , , .

Probability[pred1pred2,]
gives the conditional probability of given .

Details and OptionsDetails and Options

  • can be entered as x EscdistEsc dist or .
  • can be entered as EsccondEsc or .
  • For a continuous distribution dist, the probability of pred is given by where 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 where 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 and multivariate data is given as a list of vectors .
  • Probability[pred,{x1dist1,x2dist2}] corresponds to Probability[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
Introduced in 2010
(8.0)