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When we toss a fair coin, we expect that we get roughly half-and-half Hs and Ts. Of course, this might not happen in general: the problem is, how bad can the difference get ?
Consider a sequence of 2n coin tosses, and let X H be the number of heads and X T be the number of Ts in the resulting sequence. Obviously, EX H = EX T = n, and therefore E(X H - X T ) = 0. Show that for any ε > 0, there exists a constant c such that Pr[X H - X T > c√ n] ≤ ε

Note the quantification: in general, c will be a function of ε.
HINT: Use a Chebyshev bound.

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Computer Engineering, Engineering

Category:- Computer Engineering
Reference No.:- M9117737

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