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Random walk question

  1. Sep 30, 2007 #1
    1. The problem statement, all variables and given/known data

    Let (X1, X2, ..., Xn,...) be iid increments (with mean µ and variance ∂^2) of a random walk Sn=X1+X2+...+Xn. What are the expected value, variance of Sn?
    Prove that lim n-> ∞ Sn =+ ∞ if µ>0 and lim n-> ∞ Sn =- ∞ if µ<0

    2. Relevant equations

    3. The attempt at a solution
    I found that E(Sn)=nµ and Var(Sn)=n∂^2. I am not sure how to do the second part though.
  2. jcsd
  3. Sep 30, 2007 #2


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    What is the definition of lim Sn?
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