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A walker is at point zero on a straight line. The walker goes each time step $\Delta t = 1$, either one step to left (-1) or one step to right (+1), both having the probability of $\frac{1}{2}$.

Using CLT, what would be the average distance from zero after taking N steps? (N is very large.)

Thank you.

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  • $\begingroup$ Hint: a random variable taking the values $\pm1$ each with probability $\frac12$ has mean $0$ and variance $1$. $\endgroup$
    – Henry
    Commented Apr 5, 2016 at 12:12
  • $\begingroup$ Related: math.stackexchange.com/questions/103142/… $\endgroup$
    – Henry
    Commented Apr 5, 2016 at 12:13

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