Randomization in Statistics and Experimental Design
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(Boosting randomized algorithms) Imagine that you have an algorithm for solving a decision problem.Suppose that the algorithm makes a decision at random and returns the correct answer with probability(1)/(2) δ with some δ > 0, that is, it is just a bit better than a random guess. To improve the performance,we run the algorithm n times and take the majority vote. Show that, for any ϵ∈ (0, 1), the answer iscorrect with probability at least 1 - ϵ, as long as n ≥(1)/(2δ^2)ln((1)/(ϵ)).For example,
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