Variance Reduction Factor

Problem

Antithetic variates average each pair (X, X') with correlation correlation, reducing the variance of the pair mean to (1 + correlation) / 2 times the original variance. Return that factor.

Return 0.0 when correlation is outside [-1, 1].

Hint

Negative correlation between the pair halves the variance when it reaches -1.

Test cases

case 1

in: [0]

expected: 0.5

case 2

in: [0.8]

expected: 0.9

case 3

in: [-1]

expected: 0

case 4

in: [1]

expected: 1

Starter codePython

def variance_reduction_factor(correlation):
    # Your code here
    pass

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