1. Say you have a set of binary input features/variables X1, X2 . . . Xm that can be used to make aprediction about a discrete binary output variable Y (i.e. each of the Xi as well as Y only takeson values 0 or 1). In using the input features/variables X1, X2, . . . Xm to make a prediction about Y ,recall that the Na¨ıve Bayesian Classifier makes the simplifying assumption that P(X1, X2, . . . Xm|Y ) =Qmi=1P(Xi|Y ) in order to make it tractable to compute yP(X~ , Y ) =y P(X1, X2, . . . Xm|Y )P(Y ). Say thatthe first k input variables X1, X2 . . . Xk are actually all identical copies of each other, so that whenone has the value 0 or 1, they all do. Explain informally, but precisely, why this may be problematicfor the model learned by the Na¨ıve Bayesian Classifier.

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