MediumProbabilitypr-121

Second Moment Bound

Problem

The second moment method bounds the probability that a nonnegative integer variable is zero:

P(X = 0) <= Var(X) / E[X]^2.

Return the bound capped at 1.0, and 1.0 when the mean is nonpositive.

Hint

A small relative variance forces the variable to be positive.

case 1

in: [10,5]

expected: 0.05

case 2

in: [2,3]

expected: 0.75

case 3

in: [5,25]

expected: 1

case 4

in: [0,1]

expected: 1

Starter codePython

def second_moment_bound(mean, variance):
    # Your code here
    pass

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