The measure of association lambda for nominal variables (Goodman and Kruskal 1954) has V(Y) = 1 –max{π_+j} and V(Y|i) = 1 – rnax_j{π_j|i}. Interpret lambda as a proportional reduction in prediction 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.