Control Variate Variance Ratio

Problem

With a control variate correlated at level rho with the target estimator, the optimal variance reduction leaves the ratio 1 - rho^2 of the original variance.

Given the correlation coefficient rho, return the variance ratio.

Hint

Perfect correlation annihilates the variance.

Test cases

case 1

in: [0.5]

expected: 0.75

case 2

in: [0.99]

expected: 0.01990000000000003

case 3

in: [0]

expected: 1

Starter codePython

def control_variate_variance_ratio(rho):
    # Your code here
    pass

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