Lecture_20_E7_L20_Probability_F07

# Lecture_20_E7_L20_Probability_F07 - 1 E7 INTRODUCTION TO...

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E7 L20 1 E7: INTRODUCTION TO COMPUTER E7: INTRODUCTION TO COMPUTER PROGRAMMING FOR SCIENTISTS AND PROGRAMMING FOR SCIENTISTS AND ENGINEERS ENGINEERS Lecture Outline 1. Basic concepts of probability 2. Using rand to model random processes 3. Using histograms 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.

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E7 L20 2 Probability some concepts Probability some concepts Experiment : A situation whose outcome depends on chance Sample Space S The set of all possible outcomes of an experiment Example Experiment: throwing of a dice once S =
E7 L20 3 Probability - events Probability - events Experiment: throwing of a dice once S = Outcomes : elements of the sample space S Events : Are subsets of the sample space S Empty subsets are null or impossible events An event occurs if any of the outcomes in that event occurs.

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E7 L20 4 Probability - events Probability - events Experiment: throwing of a dice once Some events: The event of observing an even number of dots: The event O of observing an odd number of dots: S = E = O =
E7 L20 5 Probability - Sample space, outcome, event Probability - Sample space, outcome, event Experiment: throwing a pair of dice (one red and one blue ) the sample space has 36 outcomes: S = The event L of obtaining the number 7 is { } ( , ),( , ),( , ),( , ),( 1 2 3 4 5 6 5 4 3 2 , ),( ) 1 6 , L = occurs if any of the outcomes in occurs.

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Probability Probability 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 6
Probability Probability 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 An event with probability of 1 is a certain event. the sun will set tonight a person eventually dies E7 L20 7

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Assigning Probability - frequentist approach Assigning Probability - frequentist approach An experiment is repeated n times under essentially identical conditions if the event A occurs m times, then as n grows large E7 L20 8 ( ) m P A n
E7 L20 9 Dice example Dice example Experiment: throwing of a fair dice once S = { } 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 P(odd number) = 3/6 = 1/2

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Random numbers – matlab simulation Random numbers – matlab simulation Matlab rand function generates a uniformly distributed pseudo-random number between [0,1]
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Lecture_20_E7_L20_Probability_F07 - 1 E7 INTRODUCTION TO...

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