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I've been doing some research on random walks. From what I have gathered, a random walker in 1-D will have:

<x> = N l (2 p - 1)

σ = 2 l sqrt[N p (1 - p) ]

Here, N is the number of steps, p is the probability to take a step to the right and l is the step size.

I was wondering what <x^2> would be. From what I found, it seems to be l sqrt(N) but when I try to use <x^2> = σ^2 + <x>^2 , I dont get l sqrt(N) . I would like to know what <x^2> really is for an unbiased random walk.

Thanks

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# Mean squared distance traveled by an unbiased random walker in 1-D?

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