2.40 The measure of association lambda for nominal variables (Goodman and Kruskal 1954) has V (Y) = 1 - max{π+_j} and V(Y\i) = 1 - max_j{π_j|i }. Interpret lambda as a proportional reduction in error for predictions which select the response category that is most likely. Show that independence implies λ = 0 but that the converse is not true.