Jensen Gap for the Square

Problem

For the convex function f(x) = x^2, Jensen's inequality gives E[f(X)] >= f(E[X]), and the gap equals the population variance.

Given a list of samples, return mean(x^2) - mean(x)^2.

Hint

The Jensen gap for the square is the variance of the samples.

case 1

in: [[0,0]]

expected: 0

case 2

in: [[0,2]]

expected: 1

case 3

in: [[1,3]]

expected: 1

case 4

in: [[-1,1]]

expected: 1

case 5

in: [[2,2,2]]

expected: 0

Starter codePython

def jensen_gap_square(samples):
    # Your code here
    pass

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