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In class, we saw that if we have two labels, then the error of a classifier which guesses completely randomly is 0.5. in this problem,
In class, we saw that if we have two labels, then the error of a classifier which guesses completely randomly is 0.5. in this problem, we look at what happens when there are k > 2 labels. Random guesser Gezer knows that there are k labels, and for each example, selects a label out of {1.., k} uniformly at random. What is the error of Gezer? Now suppose we have a more sophisticated random guesser Zebulon who knows that w_1 fraction of the data distribution has label 1, w_2 fraction has label 2, and so on. For each example, Zebulon also selects a label out of {1, ..., k} at random, but he selects label 1 with probability w_1, label 2 with probability w_2 and so on. What is the error of Zebulon
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