Law of Total Variance

Problem

Decompose the variance of X given conditional means, conditional variances and the probabilities of the conditioning events:

Var(X) = E[Var(X | Y)] + Var(E[X | Y]).

All three input lists have the same length. An empty input returns 0.0.

Hint

Compute the overall mean first, then the two variance pieces.

case 1

in: [[0,10],[1,1],[0.5,0.5]]

expected: 26

case 2

in: [[2,4],[3,5],[0.25,0.75]]

expected: 5.25

case 3

in: [[1,1,1],[2,3,4],[0.3333333333333333,0.3333333333333333,0.3333333333333333]]

expected: 3

case 4

in: [[],[],[]]

expected: 0

Starter codePython

def law_of_total_variance(cond_means, cond_vars, probs):
    # Your code here
    pass

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