Where is the Particle

After a long time can we locate our particle? No. We cannot know where it is. How about on the average? On the average how far has our particle progressed from where it started? Remember, the mean square of the distance traveled in the sequence of random steps is the sum of the separate distances. So if vector N is the vector distance from our origin after N steps, the mean square of the distance is proportional to N, the number of steps.

But is the distance proportional to the time? If this were true, the particle would have to have progressed at a uniform velocity. So each hundredth of a second the particle makes headway but only so much headway that our particle's mean square distance is proportional to time taken.

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