E7_Lecture22_F08_Probability

E7_Lecture22_F08_Probability - 1 E7: INTRODUCTION TO...

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1 E7: INTRODUCTION TO COMPUTER ROGRAMMING FOR SCIENTISTS AND PROGRAMMING FOR SCIENTISTS AND ENGINEERS Lecture Outline 1. Basic concepts of probability sing rand to model random processes 2. Using rand to model random processes 3. Using histograms opyright 2007 Horowitz Packard This work is licensed under the Creative Commons Attribution- hare E7 L20 Copyright 2007, Horowitz, Packard. This work is licensed under the Creative Commons Attribution Share Alike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/2.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. 2 Probability some concepts xperiment Experiment : A situation whose outcome depends on chance Sample Space S he set of ll possible utcomes f an The set of all possible outcomes of an experiment Example xperiment: rowing of a dice once Experiment: throwing of a dice once = E7 L20 S = 3 Probability - events events Experiment: throwing of a dice once S = Outcomes : elements of the sample space S Events : Are subsets of the sample space S An event occurs if any of the outcomes in that event occurs. E7 L20 Empty subsets are null or impossible events 4 Probability - events events xperiment: rowing of a dice once Experiment: throwing of a dice once = Some events: S The event E of observing an even number of dots: E = The event O of observing an odd number of dots: E7 L20 O =
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5 Probability - Sample space, outcome, event Sample space, outcome, event xperiment: rowing a pair of dice (one d nd one lue Experiment: throwing a pair of dice (one red and one blue) the sample space has 36 outcomes: S = he event f obtaining the number The event L of obtaining the number 7 is { } ( , ),( , ),( , ),( , ),( 12345 65432 ,) , ( ) 1 6 , L = E7 L20 L occurs if any of the outcomes in L occurs. Probability number between 0 and 1 inclusive that indicates 6 A number between 0 and 1, inclusive, that indicates how likely an event is to occur . – An event with probability of 0 is a null event. – An event with probability of 1 is a certain event. • Probability of event A is denoted as P(A) . • The closer P(A) to 1, the more likely is A to happen. E7 L20 Probability number between 0 and 1 inclusive that indicates 7 A number between 0 and 1, inclusive, that indicates how likely an event is to occur . • An event with probability of 0 is a null event. – a man gets pregnant – a woman dies of prostate cancer p n event with probability of 1 is a ertain event. An event with probability of 1 is a certain event. – the sun will set tonight – a person eventually dies E7 L20 Assigning Probability Assigning Probability - frequentist frequentist approach approach 8 • An experiment is repeated n times under essentially identical conditions • if the event A occurs m times, then as n grows large () m PA n E7 L20
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9 Dice example xperiment: rowing of a ir ice once Experiment: throwing of a fair dice once S = 2,3,4,5,6 = { } 1,2,3,4,5,6 S P(S) = 1 P(1) = 1/6, P(3) =1/6, P(6) = 1/6 P(even number) = 3/6 = 1/2 E7 L20 P(odd number) = 3/6 = 1/2 Random numbers Random numbers – matlab simulation
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This note was uploaded on 11/01/2009 for the course ENGLISH 7 taught by Professor Sengupta during the Spring '09 term at Berkeley.

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E7_Lecture22_F08_Probability - 1 E7: INTRODUCTION TO...

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