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Create a Continuous Random Variable with an arcsin distribution.

The density of the arcsin distribution is given by

.. math::
    f(x) := \frac{1}{\pi\sqrt{(x-a)(b-x)}}

with :math:`x \in [a,b]`. It must hold that :math:`-\infty < a < b < \infty`.

Parameters(more...)

        def Arcsin(name, a=0, b=1):
    r"""
    Create a Continuous Random Variable with an arcsin distribution.

    The density of the arcsin distribution is given by

    .. math::
        f(x) := \frac{1}{\pi\sqrt{(x-a)(b-x)}}

    with :math:`x \in [a,b]`. It must hold that :math:`-\infty < a < b < \infty`.

    Parameters
    ==========

    a : Real number, the left interval boundary
    b : Real number, the right interval boundary

    Returns
    =======

    A RandomSymbol.

    Examples
    ========

    >>> from sympy.stats import Arcsin, density
    >>> from sympy import Symbol, simplify

    >>> a = Symbol("a", real=True)
    >>> b = Symbol("b", real=True)
    >>> z = Symbol("z")

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

    >>> density(X)(z)
    1/(pi*sqrt((-a + z)*(b - z)))

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Arcsine_distribution
    """

    return rv(name, ArcsinDistribution, (a, b))
        


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_arcsin():
    a = Symbol("a", real=True)
    b = Symbol("b", real=True)
 
    X = Arcsin('x', a, b)