7.2 Let X and Y have twice differentiable densities f0 and g0, and f and g

be the respective densities of Z1 = X +

p

V and Z2 = Y +

p

V, where V is independent of X and Y and EV = 0, EV 2 = 1. If X Y and

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then d lim x+2 dz [fo (2) log (fo(2))]. = 0, where D(fs.98)| = {(Vlog (Z) - Vlog g(Z))"} 8=0+ D(f,9)= log (4) f(z)dz is the Kullback-Leibler divergence of f,g and V log f(x) (2009).) = (*). (Guo