Polya Urn Variance

Problem

Variance of the number of red balls after n draws from a Polya urn that starts with r red and b blue balls:

Var = n * r * b * (r + b + n) / ((r + b)^2 * (r + b + 1)).

Return 0.0 when the urn is empty or n < 0.

Hint

The draws are positively correlated, so the variance exceeds the binomial case.

case 1

in: [1,1,1]

expected: 0.25

case 2

in: [1,1,2]

expected: 0.6666666666666666

case 3

in: [2,3,5]

expected: 2

case 4

in: [0,5,3]

expected: 0

Starter codePython

def polya_urn_variance(r, b, n):
    # Your code here
    pass

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