Conditioned

Conditioned[expr,cond]

or exprcond represents expr conditioned by the predicate cond.

Details

Examples

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Basic Examples  (2)

Compute the probability of a conditional event:

Use NProbability to get the numerical value directly:

Compute a conditional expectation:

Use NExpectation to get the numerical value directly:

Scope  (3)

Compute a conditional expectation for a discrete distribution:

Continuous distribution:

Derived distribution:

Data distribution:

Multivariate distribution:

Use implicit time to compute a conditional probabiity for a random process:

Obtain the same result using the corresponding slice distribution:

Conditional probability for a multivariate slice of a random process using implicit times:

Obtain the same result using the corresponding multivariate slice distribution:

Properties & Relations  (4)

A conditional probability is a ratio of two probabilities:

The conditional probability is 0 if the events are mutually exclusive:

Compute the probability of an event in a TruncatedDistribution:

Obtain the same result using a conditional probability calculation:

For independent variables, a conditional probability is the same as unconditional probability:

Possible Issues  (1)

Conditioned has lower precedence than And:

Use parentheses to obtain the intended result:

Wolfram Research (2010), Conditioned, Wolfram Language function, https://reference.wolfram.com/language/ref/Conditioned.html.

Text

Wolfram Research (2010), Conditioned, Wolfram Language function, https://reference.wolfram.com/language/ref/Conditioned.html.

BibTeX

@misc{reference.wolfram_2020_conditioned, author="Wolfram Research", title="{Conditioned}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/Conditioned.html}", note=[Accessed: 24-February-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_conditioned, organization={Wolfram Research}, title={Conditioned}, year={2010}, url={https://reference.wolfram.com/language/ref/Conditioned.html}, note=[Accessed: 24-February-2021 ]}

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