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 nonarithmetic. 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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 Spring '08
 Moon,J
 Computer Science, Electrical Engineering, Probability theory, Markov chain, Gallager, Gallager’s notes

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