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# sympy.stats.Uniform

All Samples(5)  |  Call(4)  |  Derive(0)  |  Import(1)
Create a continuous random variable with a uniform distribution.

The density of the uniform distribution is given by

.. math::
f(x) := \begin{cases}
\frac{1}{b - a} & \text{for } x \in [a,b]  \\
0               & \text{otherwise}
\end{cases}
(more...)


        def Uniform(name, left, right):
r"""
Create a continuous random variable with a uniform distribution.

The density of the uniform distribution is given by

.. math::
f(x) := \begin{cases}
\frac{1}{b - a} & \text{for } x \in [a,b]  \\
0               & \text{otherwise}
\end{cases}

with :math:x \in [a,b].

Parameters
==========

a : Real number, :math:-\infty < a the left boundary
b : Real number, :math:a < b < \infty the right boundary

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import Uniform, density, cdf, E, variance, skewness
>>> from sympy import Symbol, simplify

>>> a = Symbol("a", negative=True)
>>> b = Symbol("b", positive=True)
>>> z = Symbol("z")

>>> X = Uniform("x", a, b)

>>> density(X)(z)
Piecewise((1/(-a + b), And(a <= z, z <= b)), (0, True))

>>> cdf(X)(z)
-a/(-a + b) + z/(-a + b)

>>> simplify(E(X))
a/2 + b/2

>>> simplify(variance(X))
a**2/12 - a*b/6 + b**2/12

References
==========

.. [1] http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29
.. [2] http://mathworld.wolfram.com/UniformDistribution.html
"""

return rv(name, UniformDistribution, (left, right))


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_uniform():
l = Symbol('l', real=True, bounded=True)
w = Symbol('w', positive=True, bounded=True)
X = Uniform('x', l, l + w)

assert simplify(E(X)) == l + w/2
assert simplify(variance(X)) == w**2/12


# With numbers all is well
X = Uniform('x', 3, 5)
assert P(X < 3) == 0 and P(X > 5) == 0
assert P(X < 4) == P(X > 4) == S.Half