Answer Happy

Let Âmk represent the proportion of training observation in the m-th region that are from the k-th K class in a classification problem. Consider the Gini Index G = Σk=1 Pmk (1 − Îmk) and Entropy K D = − Σk-1 Ômk ln(Âmk). Suppose that K = 2. a. Show that if Âm1 = P, then G = 2p(1 − p). b. Show that if Âm1 = p, then D = −pln(p) – (1 − p)ln(1 − p). C. Show that D > G for all values of p where 0 < p<1