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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 27T

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Question

We consider a sequence (X^)^-1 of independent random variables such that
P(X=1)=1- P(Xn = −1) = Pn.
n
For all n < N, let So = 0 and S₁ == > X₂. We also consider the filtration (F)-1 given
by
i=1
Fn=σ(X1,..., Xn).

(d) Is there a choice of the values of pn (n> 1) such that (S2) 0 is a martingale ?
(e) Consider the process (V)-1 defined by
n
ΔΥΠ
Vn ==
=
ASn
Prove that (n)=1 is previsible.
Yn - Yn-1
Sn - Sn-1

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