A probability distribution on the real line is a mixture of two classes +1 and−1 with density N(0,1) (normal distribution with mean0 and variance 1) and N(3,1), with prior probabilities (probability of each class) 0.4 and 0.6 respectively. What is the Bayes decision rule? Give an estimate for the Bayes risk.

Consider the setting of the previous problem. Estimate the expected loss of the 1-NN classifier (assume that infinitely many training data points are available). What is the empirical loss of 1-NN?

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