04-Principles

04-Principles - Probability Preview and Principles EE122...

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1 Probability, Preview, and Principles EE122 Fall 2011 Scott Shenker http://inst.eecs.berkeley.edu/~ee122/ Materials with thanks to Jennifer Rexford, Ion Stoica, Vern Paxson and other colleagues at Princeton and UC Berkeley

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Announcements • Sections this week! • Shaddi Hasan • We have new account forms – Get them after class, one per person, no exceptions • Project will be released on Wednesday – So we can get to Reliable Transport beforehand • Problem 3.iii Consider case where F and Q increase, but H and P stay constant. • Waiting list: No way to move more students in – Could try doing a 194…… 2
Outline • Primer on probability (6 slides) – Simple, but all you need…. • Discussion of Homework #1 • Layering • Design Principles for the Internet – Layering – E2E Principle – Fate Sharing 3

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Probability Primer Get out a sheet of paper or otherwise be able to jot down your answers This is not a test, this is so you can tell if you understand the material
Independent Events • Independent: occurrence of one event does not affect the likelihood of the other event • Example of two independent events: – Flow 1 sends 5 packets in a particular frame – Flow 2 sends 2 packets in a particular frame • Assume that: – Event A happens with probability p A – Event B happens with probability p B • What is probability both event A and B happen? Write it down! • Answer: Probability = p A p B 5

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Consider Dice • Probability that rolling a single die yields a 1? 1/6 th • Probability rolling two dice yields 1 1? 1/36 th • Probability rolling two dice yields a 1 and a 2? Write it down! 6
Be Careful Counting Events First die is 1 and second die is 2: 1/36 th One die is 1 and one die is 2: 1/18 th • That’s because you could have 1 2 or 2 1 7

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Mutually Exclusive Events • First roll of die is 1:1/6 th • First roll of die is 2:1/6 th • First roll of die is 3:1/6 th • First roll of die is 4:1/6 th • First roll of die is 5:1/6 th • First roll of die is 6:1/6 th • This set of events is complete (or exhaustive) in that one of them must be true Total of probabilities = 1 8
Exclusive vs Independent Events • First roll of die is 1, second roll of die is 3 – Independent • First roll of die is 1, first roll of die is 2 – Exclusive 9

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Computing Averages • Assume that x is some property of an event and that events A, B, C are mutually exclusive and complete (i.e., one of them happens) – E.g., x = number of packets sent in a particular frame • Assume that: – Event A has x=5 – Event B has x=2 – Event C has x=10 • What is the average value of x? (denoted by <x>) Write it down! • Average <x> = 5p A + 2p B + 10p C 10
THIS IS ALL YOU NEED TO KNOW! • The problems are easier than you think… • …but think clearly before computing the answer… 11

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Discussion of HW#1
#2: Statistical Multiplexing • Time is divided into “frames”, frames into “slots” • Each flow is assigned one slot per frame • The flows have identical proabilistic behavior:

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