Consider a random walk in one dimension. In a single step the probability of a displacement between x and x + dx is given by

After N steps the displacement of the walker is SX++XN, where X, is the displacement during the ith step. Assume the steps are independent of one another. After N steps,

(a) what is the probability density for the displacement, S, of the walker and

(b) what are the average displacement, (S), and the standard deviation of the walker?

Transcribed Image Text:

1 (x-a)) P(x)dx exp 2O 202