This problem investigates how changing the error measurement can change the result of the learning process. You have N data points y1 y2 ... < yn and wish to estimate a representative value. (a) If your algorithm is to find the hypothesis h that minimizes the in-sample sum of squared deviations N Ein (h)=(h-yn), n=1 then show that your estimate will be the in-sample mean, N 1 h= Yn- N n=1 (HINT: For a quadratic formula, ax + bx + c, if a > 0, then the minimum point occurs at x=) (b) If your algorithm is to find the hypothesis h that minimizes the in-sample sum of absolute deviations N Ein (h) = hyn, n=1 then show that your estimate will be the in-sample median. The median point is any value for which half the data points are at most hmedian and half the data points are at least hmedian. (c) Suppose one of the data points, say yN, is perturbed to yN+e, where < is a large number. This point then becomes an outlier. What happens to your hypotheses?