1.6. If {X/1, .-0/1} and {X~, .-'l'n} are martingales, then so is {Xn + X~, ~}. But...

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1.6. If {X/1, .-0/1} and {X~, .-'l'n} are martingales, then so is {Xn + X~, ~}.

But it may happen that {X /1} and {X~} are martingales while {X n + X~} is not.

[HINT: Let XI and xi be independent Bemoullian r.v.'s; and X2

= x; = +1 or -1 according as XI

+ xi = 0 or =f. 0; notation as in (7).]

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