# Distributed

Distributed[x,dist]

or xdist asserts that the random variable x is distributed according to the probability distribution dist.

Distributed[{x1,x2,},dist]

or {x1,x2,}dist asserts that the random vector {x1,x2,} is distributed according to the multivariate probability distribution dist.

# Details

• xdist can be entered as x dist dist x \[Distributed] dist .
• xdist is a symbolic object used in functions such as Probability and Expectation.
• xproc[t] asserts that the random variable x is distributed according to the distribution SliceDistribution[proc,t] for the random process proc.
• The probability distribution dist can be any symbolic probability distribution specification.

# Examples

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## Basic Examples(3)

Compute the probability of an event in a symbolic probability distribution:

Obtain the numerical value directly using NProbability:

Compute the expectation of a function in a multivariate probability distribution:

Mean and variance for the distribution obtained by transformation of a random variable:

## Scope(5)

Compute an expectation for a parametric distribution:

Derived distribution:

Formula distribution:

Data distribution:

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

Obtain the same result using the corresponding slice distribution:

Compute an expectation for a multivariate slice of a random process:

Define a TransformedProcess:

Compute an expectation for a time slice of the process:

Simulate a TransformedProcess:

## Generalizations & Extensions(1)

Compute a probability for a distribution specified as a list:

Compare with the probability using the distribution itself:

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

#### Text

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

#### CMS

Wolfram Language. 2010. "Distributed." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Distributed.html.

#### APA

Wolfram Language. (2010). Distributed. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Distributed.html

#### BibTeX

@misc{reference.wolfram_2024_distributed, author="Wolfram Research", title="{Distributed}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/Distributed.html}", note=[Accessed: 14-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_distributed, organization={Wolfram Research}, title={Distributed}, year={2010}, url={https://reference.wolfram.com/language/ref/Distributed.html}, note=[Accessed: 14-September-2024 ]}