Runs Test Expectation and Variance

Problem

For a uniformly random binary sequence with n1 ones and n2 zeros, return [expected runs, variance of runs]:

E[R] = 2 * n1 * n2 / (n1 + n2) + 1 Var[R] = 2 * n1 * n2 * (2 * n1 * n2 - n1 - n2) / ((n1 + n2)^2 * (n1 + n2 - 1)).

If either count is 0, return [1.0, 0.0] for a nonempty sequence and [0.0, 0.0] for an empty one.

Hint

Runs are counted by the number of value alternations plus one.

case 1

in: [5,5]

expected: [6,2.2222222222222223]

case 2

in: [3,7]

expected: [5.2,1.4933333333333334]

case 3

in: [1,1]

expected: [2,0]

case 4

in: [0,5]

expected: [1,0]

Starter codePython

def runs_test_statistic(n1, n2):
    # Your code here
    pass

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