def test_density(): x = Symbol('x') l = Symbol('l', positive=True) rate = Beta(l, 2, 3) X = Poisson(x, rate) assert isinstance(pspace(X), ProductPSpace) assert density(X, Eq(rate, rate.symbol)) == PoissonDistribution(l)
def test_Poisson(): l = 3 x = Poisson('x', l) assert E(x) == l assert variance(x) == l assert density(x) == PoissonDistribution(l) assert isinstance(E(x, evaluate=False), Sum) assert isinstance(E(2 * x, evaluate=False), Sum)
def test_PoissonDistribution(): l = 3 p = PoissonDistribution(l) assert abs(p.cdf(10).evalf() - 1) < .001 assert p.expectation(x, x) == l assert p.expectation(x**2, x) - p.expectation(x, x)**2 == l