# Random walk question

1. Sep 30, 2007

### erica1451

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. Sep 30, 2007

### EnumaElish

What is the definition of lim Sn?