Cauchy PDF

Problem

Cauchy probability density with location x0 and scale gamma:

f(x) = 1 / (pi * gamma * (1 + ((x - x0) / gamma)^2)).

Return 0.0 for gamma <= 0.

Hint

Standardize x with z = (x - x0) / gamma first.

case 1

in: [0,1,0]

expected: 0.3183098861837907

case 2

in: [0,1,1]

expected: 0.15915494309189535

case 3

in: [0,2,0]

expected: 0.15915494309189535

case 4

in: [0,0,0]

expected: 0

Starter codePython

import math


def cauchy_pdf(x0, gamma, x):
    # Your code here
    pass

4 test cases · run your code against them in the editor