1. Suppose that I'm flipping a dime and quarter, such that the probability that both are head is pi, both tail is P2, only the dime is head is p3, and only the quarter is head is 1- P1 – P2 - p3. The entropy (or randomness) of this two-coin-flip is H(P1, P2, P3) = -pı log2 (P1) – P2 log2 (P2) – P3 log2 (P3) – (1 – P1 – P2 - P3) log2(1 – P1 – P2 - P3). Calculate a H/Op1, and evaluate it at P1 = P2 = P3 = 0.25 and at pı = 0.7, P2 = P3 = 0.1. 2. Compute the Hessian of the following functions, and verify directly that the matrix is symmetric: (a) u(x, y) = y*exy, (b) v(x, y, s) = 114,22 3. I'm climbing a mountain, whose landscape is described by the function z(x, y) = e-(x++y). I'm at position (x, y) = (-1,1). What is the maximal slope at this point? What is the slope I'm climbing if I walk southwest?