# 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

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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: