consider the setting of the polynomial regression in example use theorem to prove that - - ( bn - ` - ( where : [xx( (xgg ( )) is the matrix with (ij)-th entryz inverse hilbert matrix uij- (hh (uh( )) duand - is the inverse hilbert matrix with (ij)-th entry! + - pj- ij- (- ( - - pj ij observe that for so that the matrix term is due to choosing restrictive class that does not contain the true prediction function in example we saw that the statistical error can be expressed (see ( )as  [ - ]( du ( ) ( by exercise the random vector : ( bn has asymptotically multivariate - - normal distribution with mean vector and covariance matrix :` - hp mphp use theorem to show that the expected statistical error is asymptotically ( ) ( bpn tr( - ( plot this large-sample approximation of the expected statistical error and compare it with the outcome of the statistical error we note subtle technical detailin generalconvergence in distribution does not imply convergence in -norm (see example )and so here we have implicitly assumed that kz -dist kz -constant :limnekz consider again example the result in ( suggests that as where is the solution in the class given in ( thusthe large-sample approximg at [ - ]is ation of the pointwise bias of the learner gt (xx> gt (xg( [ - [ uu bn use python to reproduce figure which shows the (large-samplepointwise squared bias of the learner for { note how the bias is larger near the endpoints and explain why the areas under the curves correspond to the approximation errors