Conditioned[expr,cond]
or exprcond represents expr conditioned by the predicate cond.
Conditioned 
Conditioned[expr,cond]
or exprcond represents expr conditioned by the predicate cond.
Details
- exprcond can be entered as expr
cond
cond or expr \[Conditioned] cond. - The expression expr can correspond either to a predicate with logical values or to an object with numerical values.
- Probability[predcond,…] gives the conditional probability of pred given cond.
- Expectation[exprcond,…] gives the conditional expectation of expr given cond.
- Conditioned can be used in functions such as Probability, NProbability, Expectation, and NExpectation.
Examples
open all close allBasic Examples (2)
Compute the probability of a conditional event:
Probability[x ^ 2 > 12x > 2, xPoissonDistribution[2]]N[%]Use NProbability to get the numerical value directly:
NProbability[x ^ 2 > 12x > 2, xPoissonDistribution[2]]Compute a conditional expectation:
Expectation[x ^ 5x > 2, xNormalDistribution[]]N[%]Use NExpectation to get the numerical value directly:
NExpectation[x ^ 5x > 2, xNormalDistribution[]]Scope (3)
Compute a conditional expectation for a discrete distribution:
Expectation[x ^ 2 + 3xx > 1, xPoissonDistribution[μ]]Expectation[x ^ 2 + 3xx > 1, xExponentialDistribution[3]]Expectation[x ^ 2 + 5x > 1, xTransformedDistribution[x ^ 3, xExponentialDistribution[2]]]data = RandomVariate[NormalDistribution[], 10^4];𝒟 = HistogramDistribution[data];Expectation[x ^ 2x > 2, x𝒟]Expectation[x ^ 2 + y(x + y > 1), {x, y}UniformDistribution[{{-1, 1}, {-2, 2}}]]Use implicit time to compute a conditional probabiity for a random process:
NProbability[x[1] > 7x[1] > 1, xPoissonProcess[4]]Obtain the same result using the corresponding slice distribution:
NProbability[x > 7x > 1, xPoissonProcess[4][1]]Conditional probability for a multivariate slice of a random process using implicit times:
Probability[x[5] > 1x[3] == 1 / 5, xWienerProcess[1 / 5, 2]]Obtain the same result using the corresponding multivariate slice distribution:
Probability[y > 1x == 1 / 5, {x, y}WienerProcess[1 / 5, 2][{3, 5}]]Properties & Relations (4)
A conditional probability is a ratio of two probabilities:
expr1 = x ^ 2 < 30;expr2 = x > 1;Probability[expr1expr2, xPoissonDistribution[2]]Probability[expr1 && expr2, xPoissonDistribution[2]] / Probability[expr2, xPoissonDistribution[2]]The conditional probability is 0 if the events are mutually exclusive:
expr1 = 3 < x < 5;expr2 = x > 7;Probability[expr1expr2, xPoissonDistribution[2]]Probability[expr2expr1, xPoissonDistribution[2]]Compute the probability of an event in a TruncatedDistribution:
Probability[x ^ 2 > 1, xTruncatedDistribution[{-2, 3}, NormalDistribution[]]]N[%]Obtain the same result using a conditional probability calculation:
Probability[x ^ 2 > 1 -2 < x < 3, xNormalDistribution[]]N[%]For independent variables, a conditional probability is the same as unconditional probability:
𝒟 = UniformDistribution[{{-3, 4}, {2, 5}}];Probability[x > 3y > 1, {x, y}𝒟]Probability[x > 3, {x, y}𝒟]See Also
Probability NProbability Expectation NExpectation
Characters: \[Conditioned]
Function Repository: ConditionedMultinormalDistribution
Related Guides
History
Text
Wolfram Research (2010), Conditioned, Wolfram Language function, https://reference.wolfram.com/language/ref/Conditioned.html.
CMS
Wolfram Language. 2010. "Conditioned." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Conditioned.html.
APA
Wolfram Language. (2010). Conditioned. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Conditioned.html
BibTeX
@misc{reference.wolfram_2026_conditioned, author="Wolfram Research", title="{Conditioned}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/Conditioned.html}", note=[Accessed: 13-June-2026]}
BibLaTeX
@online{reference.wolfram_2026_conditioned, organization={Wolfram Research}, title={Conditioned}, year={2010}, url={https://reference.wolfram.com/language/ref/Conditioned.html}, note=[Accessed: 13-June-2026]}