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All Samples(8)  |  Call(6)  |  Derive(0)  |  Import(2)
Cumulative Distribution Function of a random expression.

optionally given a second condition

This density will take on different forms for different types of
probability spaces.
Discrete variables produce Dicts.
Continuous variables produce Lambdas.

Examples(more...)

        def cdf(expr, condition=None, evaluate=True, **kwargs):
    """
    Cumulative Distribution Function of a random expression.

    optionally given a second condition

    This density will take on different forms for different types of
    probability spaces.
    Discrete variables produce Dicts.
    Continuous variables produce Lambdas.

    Examples
    ========

    >>> from sympy.stats import density, Die, Normal, cdf
    >>> from sympy import Symbol

    >>> D = Die('D', 6)
    >>> X = Normal('X', 0, 1)

    >>> density(D).dict
    {1: 1/6, 2: 1/6, 3: 1/6, 4: 1/6, 5: 1/6, 6: 1/6}
    >>> cdf(D)
    {1: 1/6, 2: 1/3, 3: 1/2, 4: 2/3, 5: 5/6, 6: 1}
    >>> cdf(3*D, D>2)
    {9: 1/4, 12: 1/2, 15: 3/4, 18: 1}

    >>> cdf(X)
    Lambda(_z, erf(sqrt(2)*_z/2)/2 + 1/2)
    """
    if condition is not None:  # If there is a condition
        # Recompute on new conditional expr
        return cdf(given(expr, condition, **kwargs), **kwargs)

    # Otherwise pass work off to the ProbabilitySpace
    result = pspace(expr).compute_cdf(expr, **kwargs)

    if evaluate and hasattr(result, 'doit'):
        return result.doit()
    else:
        return result
        


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_cdf():
    X = Normal('x', 0, 1)
 
    d = cdf(X)
    assert P(X < 1) == d(1)
    assert d(0) == S.Half
 
    d = cdf(X, X > 0)  # given X>0
 
    Y = Exponential('y', 10)
    d = cdf(Y)
    assert d(-5) == 0
    assert P(Y > 3) == 1 - d(3)
 
    raises(ValueError, lambda: cdf(X + Y))

src/s/y/sympy-HEAD/sympy/stats/tests/test_finite_rv.py   sympy(Download)
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,
 
    assert cdf(
        D) == sympify({1: o/6, 2: o/3, 3: o/2, 4: 2*o/3, 5: 5*o/6, 6: o})