MediumProbabilitypr-403

Cantelli One Sided Bound

Problem

Cantelli's inequality bounds one tail: P(X - mu >= t) <= sigma^2 / (sigma^2 + t^2).

Given the variance and the offset t > 0, return the bound.

Hint

It is tighter than Chebyshev for a single direction.

case 1

in: [1,1]

expected: 0.5

case 2

in: [4,2]

expected: 0.5

case 3

in: [0.25,3]

expected: 0.02702702702702703

Starter codePython

def cantelli_one_sided_bound(variance, t):
    # Your code here
    pass

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