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

open allclose all

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:

Introduced in 2010
 (8.0)