Consider training data ((xi, yi)li=1.n, where x; E IRd and y; E (0, 1). Consider the logistic data model y = o(0 . x), where x E IRd, O E IRd, and o is the logistic function o(z) = ez/(ez + 1). (a) Show that o'(z) = o(z) (1 - o(z)). Response: (b) Let f(0) = ET_1-y; logy; -(1-y;) log(1 -y;), where y; = o(0 . x;). Compute Vf(0). Use the fact in part (a) to simplify your answer. Response: (c) If M = El_ xix., show that z*Mz 2 0 for any z E IRd. Response: (d) Using a summation and vector and / or matrix products, write down a formula for the Hessian, H, of f with respect to 0. Show that z' Hz 2 0 for any z E IRd. Response