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I'm not quite sure what part (a) is asking.

For part (b), I'm thinking that this has something to do with Chebyshev's inequality, but the examples for Chebyshev's inequality in my textbook and notes don't involve the use of 'max {...}'. So I'm pretty much stuck. But intuitively, I think it will be 0 when n tends to infinity, but I don't really know how to prove it.