7 Let Xn n0 be a family of random variables with finite expectations that satisfy E(Xn 1 X1, ,Xn) Xn (1 )Xn1 for n 1 and some constant 1 Find a second constant so that the random variables Yn Xn Xn1 for n 1 constitute a martingale relative to Xn n0 ...

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=+7. Let {Xn}n0 be a family of random variables with finite expectations that satisfy E(Xn+1 | X1,...,Xn)

Question:

=+7. Let {Xn}n≥0 be a family of random variables with finite expectations that satisfy E(Xn+1 | X1,...,Xn) = αXn + (1 − α)Xn−1 for n ≥ 1 and some constant α = 1. Find a second constant β so that the random variables Yn = βXn + Xn−1 for n ≥ 1 constitute a martingale relative to {Xn}n≥0.

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