Question 3. (Maximal coupling on finite sample spaces) Two finite probability distributions P and Q defined on a sample space ? = {a, b, c} are given by P({a}) = 1/3, P((b}) = 1/3, P((c)) = 1/3. Q((a}) = 1/2, Q (1b}) = 1/4, Q((c}) = 1/4. Find the maximal coupling of P and Q.Question 3. (Maximal coupling on finite sample spaces) Two finite probability distributions P and Q defined on a sample space ? = {a, b, c} are given by P({a}) = 1/3, P((b}) = 1/3, P((c)) = 1/3. Q((a}) = 1/2, Q (1b}) = 1/4, Q((c}) = 1/4. Find the maximal coupling of P and