def test_maxwell():
a = Symbol("a", positive=True)
X = Maxwell('x', a)
assert density(X)(x) == (sqrt(2)*x**2*exp(-x**2/(2*a**2))/
(sqrt(pi)*a**3))
assert E(X) == 2*sqrt(2)*a/sqrt(pi)
assert simplify(variance(X)) == a**2*(-8 + 3*pi)/pi
def test_maxwell():
a = Symbol("a", positive=True)
X = Maxwell('x', a)
assert density(X)(x) == (sqrt(2)*x**2*exp(-x**2/(2*a**2))/
(sqrt(pi)*a**3))
assert E(X) == 2*sqrt(2)*a/sqrt(pi)
assert variance(X) == -8*a**2/pi + 3*a**2
assert cdf(X)(x) == erf(sqrt(2)*x/(2*a)) - sqrt(2)*x*exp(-x**2/(2*a**2))/(sqrt(pi)*a)
assert diff(cdf(X)(x), x) == density(X)(x)
def test_maxwell():
a = Symbol("a", positive=True)
x = Symbol("x")
X = Maxwell(a, symbol=x)
assert density(X) == (Lambda(
_x,
sqrt(2) * _x**2 * exp(-_x**2 / (2 * a**2)) / (sqrt(pi) * a**3)))
assert E(X) == 2 * sqrt(2) * a / sqrt(pi)
assert simplify(variance(X)) == a**2 * (-8 + 3 * pi) / pi