Question: Suppose that 10 insurance claims are examined for compliance with insurer payment policies. Suppose further that each claim will comply or not independently of the other claims. The following statistical model is proposed: Let X be the total number of compliant claims, and suppose that X has a binomial distribution with n = 10 and probability of compliance p for each claim, with p left unspecified, except that \[0\le p\le 1\]. Also, let Y be the number of noncompliant claims among the ten claims.

a) What is the probability distribution of Y? [Hint: No calculations are necessary.]

b) What is the correlation coefficient between X and Y? [Hint: No calculations are necessary – what is the relationship between X and Y?]