lecture16

# lecture16 - ECE 5510 Random Processes Lecture Notes Fall...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2008 Lecture 16 Today: (1) Poisson Processes • HW 7 due today at 5pm. OH today 1-2:40. • Exam 2 is Tue. Nov. 11. Today’s material is the last new material covered in Exam 2. Tue (Nov. 4) is a review class. AA #4 now due 5pm Wed. Nov. 5th. 1 Poisson Process Today, we will cover the right-hand column of this table: Discrete Time Continuous-Time What is this counting process called? “Bernoulli” “Poisson” How long until my first 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 ) = parenleftbigg n k n parenrightbigg p k n (1- p ) n- k n 1.2 Derivation of Poisson pmf Now, time is continuous. I want to know, how many arrivals have happened in time T . Eg, how many packets have been transmitted in my network. Here’s how but I could translate it to a Bernoulli process question: • Divide time into intervals duration T/n (eg, T/n = 1 minute). • Define the arrival of one packet in an interval as a ‘success’ in that interval. ECE 5510 Fall 2008 2 • Assume that success in each interval is i.i.d. • Sum the Bernoulli R.P. to get a Binomial process. Problem: Unless the time interval T/n is really small, you might actually have more than one packet arrive in each interval. Since Binomial can only account for 1 or 0, this doesn’t represent your total number of packets exactly. 1.2.1 Let time interval go to zero Long Story : Let’s define K ( T ) to be the number of packets which have arrived by time T for the real, continuous time process. Let’s define Y n as our Binomial approximation, in which T is divided into n identical time bins. Let’s show what happens as we divide T into more and more time bins,...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

lecture16 - ECE 5510 Random Processes Lecture Notes Fall...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online