Consider the random walk problem for a particle in one dimension. Assume that at each step its displacement is always po

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Consider The Random Walk Problem For A Particle In One Dimension Assume That At Each Step Its Displacement Is Always Po 1 (487.27 KiB) Viewed 33 times

Consider the random walk problem for a particle in one dimension. Assume that at each step its displacement is always positive and equally likely to be anywhere in the interval between l – b and l + b where b < l. o(s)ds b) Find an expression for the probability density function of the particle position after N steps, Pn(x) (Do not calculate the integral). a) Calculate Q(k)=Leikos c) In the limit N → 00, the expression for the probability density function of the position after N steps can be approximated by : 1 -ikx iNkl e-N(kb)?/6 dk einkle 21 Py(x) = e N Calculate this integral and obtain Pn(x). Does this result agree with the central limit theorem? Justify your answer. d) After N steps, what is the mean displacement and variance?