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Create a continuous random variable with a Wigner semicircle distribution.

The density of the Wigner semicircle distribution is given by

.. math::
    f(x) := \frac2{\pi R^2}\,\sqrt{R^2-x^2}

with :math:`x \in [-R,R]`.

Parameters(more...)

        def WignerSemicircle(name, R):
    r"""
    Create a continuous random variable with a Wigner semicircle distribution.

    The density of the Wigner semicircle distribution is given by

    .. math::
        f(x) := \frac2{\pi R^2}\,\sqrt{R^2-x^2}

    with :math:`x \in [-R,R]`.

    Parameters
    ==========

    R : Real number, `R > 0`, the radius

    Returns
    =======

    A `RandomSymbol`.

    Examples
    ========

    >>> from sympy.stats import WignerSemicircle, density, E
    >>> from sympy import Symbol, simplify

    >>> R = Symbol("R", positive=True)
    >>> z = Symbol("z")

    >>> X = WignerSemicircle("x", R)

    >>> density(X)(z)
    2*sqrt(R**2 - z**2)/(pi*R**2)

    >>> E(X)
    0

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Wigner_semicircle_distribution
    .. [2] http://mathworld.wolfram.com/WignersSemicircleLaw.html
    """

    return rv(name, WignerSemicircleDistribution, (R,))
        


src/s/y/sympy-HEAD/sympy/stats/tests/test_continuous_rv.py   sympy(Download)
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_wignersemicircle():
    R = Symbol("R", positive=True)
 
    X = WignerSemicircle('x', R)
    assert density(X)(x) == 2*sqrt(-x**2 + R**2)/(pi*R**2)
    assert E(X) == 0