a. (5 points) Intuitively, how do you expect the bias and variance to behave for small values of m? What about large values of m? b. [5 points) If we define f) = m ):"(-1)m+1 f(:) and the average bias-squared as , Et (Elfm(x;)] - f(x;))2, show that / m jm [( E fm(2.)] - f(z.))' = = _ E ( F() - f(Ii) ) ? j=li=(j-1)m+1 C. (5 points) If we define the average variance as E : Et(fm(x.) -Elfm(x.)])?|, show (both equalities) j=1 m d. [15 points) Let n = 256, o2 = 1, and f(x) = 4sin(x) cos(6x2). For values of m = 1, 2, 4, 8, 16, 32 plot the average empirical error , Et-(fm(x.) -f(x.)) using randomly drawn data as a function of m on the r-axis. On the same plot, using parts b and c of above, plot the average bias-squared, the average variance, and their sum (the average error). Thus, there should be 4 lines on your plot, each described in a legend. e. (Extra credit [5 points] ) By the Mean-Value theorem we have that mini=(j-1)m+1,...,jm f(I.)