16. Testing for Independence in a Bivariate Normal Population Distribution Let (X" Y,), i == I, ... , n, be a random sample from some bivariate normal population distribution N(tL, ~)

where af = ai- In this case, we know that the bivariate random variables are independent iff the correlation between them is zero. Consider testing the hypothesis of independence Ho: P == 0 versus the alternative hypothesis of dependence H,,: polO.