Fisher Information of a Gaussian

Problem

For a univariate Gaussian with known variance, the Fisher information about the mean is 1 / sigma^2, and about the standard deviation it is 2 / sigma^2.

Given sigma > 0, return the pair [I_mu, I_sigma].

Hint

The information is the expected squared score, which scales inversely with the variance.

Test cases

case 1

in: [1]

expected: [1,2]

case 2

in: [2]

expected: [0.25,0.5]

case 3

in: [0.5]

expected: [4,8]

case 4

in: [4]

expected: [0.0625,0.125]

Starter codePython

def fisher_gaussian(sigma):
    # Return [I_mu, I_sigma]
    # Your code here
    pass

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