Let X, Y be two Bernoulli random variables and denote by p = P (X = 1), q = P (Y = 1) and r = P (X = 1, Y = 1). Let {Xi, Yi} n i=1 be a sample of n i.i.d. copies of (X, Y ). Based on this sample, we...

Let X, Y be two Bernoulli random variables and denote by p = P (X = 1),      q = P (Y = 1) and r = P (X = 1, Y = 1).

 Let {Xi, Yi}ⁿ
_i=1be a sample of n i.i.d. copies of (X, Y ). Based on this sample, we want to test whether X and Y are independent, i.e., whether r =pq