6.262.PS7

6.262.PS7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.262 – Discrete Stochastic Processes Problem Set #7 Issued: March 19, 2010 Due: April 2, 2010 Reading : For this week, study Section 3.7 carefully and skim Section 3.8. For next week, begin reading Chapter 5 (which we’ll put on the web soon). 1. Exercise 3.8 in Gallager’s notes 2. Exercise 3.23 in Gallager’s notes. (Assume that N(t) is non-arithmetic. Is the result in part a) ever true for an arithmetic renewal process? Compare your results to eq. (3.36) on p. 125 of the course notes.) 3. Exercise 3.26 in Gallager’s notes. Compare the behavior of this system with that in Exercise 2.23 in Problem 2 on Pset #3. 4 . Exercise 3.27 in Gallager’s notes. 5) Two important phenomena in physics (and other fields) are drift and diffusion . Drift is the motion of a randomly perturbed particle or collection of particles when the average motion is in a single direction. The randomly perturbed motion becomes diffusion when there is no average direction of motion. The general findings are that the average time required for a particle to move a distance δ x in its average direction of motion grows linearly with δ x , i.e., drift δ x δ t = v ,where v drift is the “drift velocity,” while the average time δ t
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This note was uploaded on 10/21/2010 for the course EE 5581 taught by Professor Moon,j during the Spring '08 term at Minnesota.

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6.262.PS7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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