Random walk question

  • Thread starter erica1451
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  • #1
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Homework Statement



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

Homework Equations





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.
 

Answers and Replies

  • #2
EnumaElish
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What is the definition of lim Sn?
 

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