1. Failure of k-fold cross validation: Consider a case in which the label is chosen at random according to P[y=1]=P[y=0]=1/2. Consider a learning algorithm that outputs the constant predictor h(x)=1 if the parity of the labels on the training set is 1 and otherwise the algorithm outputs the constant predictor h(x)=0. Prove that the difference between the leave-one-out estimate and the true error in such a case is always 1/2. 2. Occam's razor: Let D be dataset, H be models and be model parameters. ^=argmaxp(D,H) Assuming a broad Gaussian prior distribution and iid observations, derive an approximation for the log evidence logp(DH), in terms of the dataset size N, 's dimensionality m, and logp(D)