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# sympy.stats.pspace

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```Returns the underlying Probability Space of a random expression.

For internal use.

Examples
========

>>> from sympy.stats import pspace, Normal
>>> from sympy.stats.rv import ProductPSpace
>>> X = Normal('X', 0, 1)(more...)
```

```        def pspace(expr):
"""
Returns the underlying Probability Space of a random expression.

For internal use.

Examples
========

>>> from sympy.stats import pspace, Normal
>>> from sympy.stats.rv import ProductPSpace
>>> X = Normal('X', 0, 1)
>>> pspace(2*X + 1) == X.pspace
True
"""

rvs = random_symbols(expr)
if not rvs:
return None
# If only one space present
if all(rv.pspace == rvs[0].pspace for rv in rvs):
return rvs[0].pspace
# Otherwise make a product space
return ProductPSpace(*[rv.pspace for rv in rvs])
```

```from sympy import (EmptySet, FiniteSet, S, Symbol, Interval, exp, erf, sqrt,
symbols, simplify, Eq, cos, And, Tuple, integrate, oo, sin, Sum, Basic,
DiracDelta)
from sympy.stats import (Die, Normal, Exponential, P, E, variance, covariance,
skewness, density, given, independent, dependent, where, pspace,
```
```def test_pspace():
X, Y = Normal('X', 0, 1), Normal('Y', 0, 1)

assert not pspace(5 + 3)
assert pspace(X) == X.pspace
assert pspace(2*X + 1) == X.pspace
assert pspace(2*X + Y) == ProductPSpace(Y.pspace, X.pspace)
```

```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_random_parameters():
mu = Normal('mu', 2, 3)
meas = Normal('T', mu, 1)
assert density(meas, evaluate=False)(z)
assert isinstance(pspace(meas), ProductPSpace)
```

```from sympy import (EmptySet, FiniteSet, S, Symbol, Interval, exp, erf, sqrt,
symbols, simplify, Eq, cos, And, Tuple, Or, Dict, sympify, binomial,
factor)
from sympy.stats import (DiscreteUniform, Die, Bernoulli, Coin, Binomial,
Hypergeometric, P, E, variance, covariance, skewness, sample, density,
```

```def test_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, where
X = Normal('x1', 0, 1)
assert str(where(X > 0)) == "Domain: x1 > 0"

```

```def test_latex_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, where
X = Normal('x1', 0, 1)
assert latex(where(X > 0)) == "Domain: x_{1} > 0"

```

```def test_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, where
X = Normal('x1', 0, 1)
assert upretty(where(X > 0)) == u("Domain: x₁ > 0")

```

```def test_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, where
X = Normal('x1', 0, 1)
assert str(where(X > 0)) == "Domain: x1 > 0"

```

```def test_latex_RandomDomain():
from sympy.stats import Normal, Die, Exponential, pspace, where
X = Normal('x1', 0, 1)
assert latex(where(X > 0)) == "Domain: x_{1} > 0"

```

```def test_RandomDomain():