Consider an ensemble learning algorithm that uses simple majority voting among M learned hypotheses. Suppose that each hypothesis has error E and that the errors made by each hypothesis are independent of the others'. Calculate a formula for the error of the ensemble algorithm in terms of M and E, and evaluate it for the cases where M = 5, 10, and 20 and E = 0.1,0.2, and 0.4. If the independence assumption is removed, is it possible for the ensemble error to be worse than E?
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