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

[CrimsonFlash]

Hey!

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 don't get l sqrt(N) . I would like to know what <x^2> really is for an unbiased random walk.

Thanks

 

[mathman]

In "l sqrt(N)", what is "l"?

 

[CrimsonFlash]

In "l sqrt(N)", what is "l"?

l is the step size here.

 

[mathman]

The second moment is proportional to l^2. In general its main use is as an intermediate to get the variance.