Entropy Power Inequality Check

Problem

Check the entropy power inequality for continuous random variables. Define the entropy power N(h) = 2^(2h) / (2 * pi * e) for a differential entropy h in bits, and return True when N(X+Y) >= N(X) + N(Y) within 1e-12.

Hint

Two independent Gaussians achieve equality in the entropy power inequality.

Test cases

case 1

in: [2.047095585180641,2.047095585180641,2.547095585180641]

expected: true

case 2

in: [2,1,2.6]

expected: true

case 3

in: [1,1,1.5]

expected: true

case 4

in: [2.047095585180641,0,1.5]

expected: false

Starter codePython

import math
def entropy_power_inequality_holds(hx, hy, hxy):
    # Your code here
    pass

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