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# sympy.stats.ContinuousRV

All Samples(3)  |  Call(2)  |  Derive(0)  |  Import(1)
```Create a Continuous Random Variable given the following:

-- a symbol
-- a probability density function
-- set on which the pdf is valid (defaults to entire real line)

Returns a RandomSymbol.

Many common continuous random variable types are already implemented.
This function should be necessary only very rarely.(more...)
```

```        def ContinuousRV(symbol, density, set=Interval(-oo, oo)):
"""
Create a Continuous Random Variable given the following:

-- a symbol
-- a probability density function
-- set on which the pdf is valid (defaults to entire real line)

Returns a RandomSymbol.

Many common continuous random variable types are already implemented.
This function should be necessary only very rarely.

Examples
========

>>> from sympy import Symbol, sqrt, exp, pi
>>> from sympy.stats import ContinuousRV, P, E

>>> x = Symbol("x")

>>> pdf = sqrt(2)*exp(-x**2/2)/(2*sqrt(pi)) # Normal distribution
>>> X = ContinuousRV(x, pdf)

>>> E(X)
0
>>> P(X>0)
1/2
"""
pdf = Lambda(symbol, density)
return SingleContinuousPSpace(symbol, dist).value
```

```from sympy.stats import (P, E, where, density, variance, covariance, skewness,
given, pspace, cdf, ContinuousRV, sample,
Arcsin, Benini, Beta, BetaPrime, Cauchy,
Chi, ChiSquared,
ChiNoncentral, Dagum, Erlang, Exponential,
```
```def test_sample():
z = Symbol('z')
Z = ContinuousRV(z, exp(-z), set=Interval(0, oo))
assert sample(Z) in Z.pspace.domain.set
sym, val = list(Z.pspace.sample().items())[0]
assert sym == Z and val in Interval(0, oo)
```
```def test_ContinuousRV():
x = Symbol('x')
pdf = sqrt(2)*exp(-x**2/2)/(2*sqrt(pi))  # Normal distribution
# X and Y should be equivalent
X = ContinuousRV(x, pdf)
```