sympy.stats.Cauchy() in Python

With the help of sympy.stats.Cauchy() method, we can get the continuous random variable which represents the cauchy distribution.

Syntax : sympy.stats.Cauchy(name, x, gamma)
Where, x and gamma is a real number and gamma is greater 0.
Return : Return the continuous random variable.

Example #1 :
In this example we can see that by using sympy.stats.Cauchy() method, we are able to get the continuous random variable representing the cauchy distribution by using this method.

# Import sympy and cauchy
from sympy.stats import Cauchy, density
from sympy import Symbol

x0 = Symbol("x0")
gamma = Symbol("gamma", positive = True)
z = Symbol("z")

# Using sympy.stats.Cauchy() method
X = Cauchy("x", x0, gamma)
gfg = density(X)(z)

print(gfg)

Output :

1/(pi*gamma*(1 + (-x0 + z)**2/gamma**2))

Example #2 :

# Import sympy and cauchy
from sympy.stats import Cauchy, density
from sympy import Symbol

x0 = 2
gamma = 3
z = 0.5

# Using sympy.stats.Cauchy() method
X = Cauchy("x", x0, gamma)
gfg = density(X)(z)

print(gfg)

Output :

0.266666666666667/pi