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Toss a symmetric coin repeatedly and set

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Since n - S_n equals the number of tails in n tosses, it follows that X_n = the number of heads minus the number of tails, that is the excess of heads over tails in n tosses. Show that {X_n, n ≥ 1} (together with the sequence of natural σ-algebras) is a martingale.

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Category:- Statistics and Probability
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