Let H (p1, . . . , pk) denote the entropy of a random variable with nite support {ch . . . , ck} and probabilities p1: = P(X = q). The entropy depends only on the probabilities, so this makes sense. (i) Show that for any (1 E [0, 1] and any choice of 131, . . . ,1)\" 6 [0,1] with 2 pi = 1 the following relation holds: H(p1. - - - ,pn_1,pnq,pn(1 - (1)) = H(p1,- - - ,pn) +an(q,1 - q)- (2-15) (ii) Consider a game where a sixsided die is rolled, and if the number 6 comes up, then a fair coin is ipped. Compute the entropy of this game directly from the denition (the left side of (2.15)), and then compute the right side of (2.15) for this game