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ECE 5510: Random Processes
Lecture Notes
Fall 2009
Lecture 16
Today: Poisson Processes: (1) Indep. Increments, (2) Expo
nential Interarrivals
•
Exam 2 is Tue. Nov. 10. Today’s material is the last new
material covered in Exam 2.
•
Tue (Nov. 3) is a of, but Appl. Assignment 4 is due Tue
Nov. 3 at midnight.
•
Thu (Nov 5) is a review class, and HW 7 is due beFore the
start oF class. Show up with questions.
1
Poisson Process
The leFt hand side oF this table covers discretetime Bernoulli and
Binomial R.P.s, which we have covered. We also mentioned the
Geometric pmF in the ±rst part oF this course. Now, we are covering
the righthand column, which answer the same questions but For
continuoustime R.P.s.
Discrete Time
ContinuousTime
What is this counting process
called?
“Bernoulli”
“Poisson”
How long until my ±rst ar
rival/success?
Geometric p.m.F.
Exponential p.d.F.
AFter a set amount oF time, how
many arrivals/successes have I
had?
Binomial p.m.F.
Poisson p.m.F.
1.1
Last Time
This is the marginal pmF oF
Y
n
during a Binomial counting process:
P
Y
n
(
k
n
) =
p
n
k
n
P
p
k
n
(1

p
)
n

k
n
1.2
Independent Increments Property
In the Binomial process,
Y
n
, we derived the pmF by assuming that
we had independent Bernoulli trials at each trial
i
. In the Poisson
process,
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View Full DocumentECE 5510 Fall 2009
2
•
If we consider any two nonoverlapping intervals, they are in
dependent. For example, consider the number of arrivals in
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 Fall '08
 Chen,R

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