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# chap2 - GE 331 Analytic methods for uncertainty IE 300...

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GE 331 Analytic methods for uncertainty IE 300 Analysis of data Liming Feng 1

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Introductory probability and statistics: analyze data, make decisions Objectives Learn basic probability/statistics concepts & techniques Learn how to conduct statistical computing Learn how to interpret results and make decisions Course objectives 2
Benzene in exit water Example: Benzene is a toxic chemical used to manufacture a wide variety of chemical products: medicinal chemicals, dyes, artificial leather. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of benzene http://www.cancer.org/docroot/PED/content/PED_1_3X_Benzene.asp?sitearea=PED 3

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Need to test the manufacturer’s claim ( hypothesis testing ) You collect 10 water samples, measure benzene content, compute the average: 7906 ppm Is the manufacturer’s claim valid Possible that the actual average content is greater than 7980 ppm Where to set the threshold 4
Statistics The science of collecting analyzing interpreting data in order to make decisions and recommendations Improve existing systems, design better products, etc. 5

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Probability Data exhibit randomness (e.g., variation of benzene content) Probability provides techniques to study randomness (e.g., measure magnitude of variation) Provides ways to quantify likelihood of events (e.g., making a wrong recommendation in the benzene example) 6
Contents Probability Chapter 2 : basics Chapter 3 : discrete random variables Chapter 4 : continuous random variables Chapter 5 : joint distributions Statistics Chapter 6 : basics Chapter 7 : estimating parameters Chapter 8 : confidence intervals Chapter 9 : testing hypotheses Chapter 10 : two samples Chapter 11 : linear regression 7

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Syllabus Basics of probability theory Chapter 2 8
Playing craps 9

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Shooter first rolls two dice ( come-out throw ), add the numbers on the dice Throwing a natural : 7 or 11 Throwing a point : 4,5,6, 8,9,10 •C r a p s : 2 ( snake eyes),3,12 (box cars ) 10
Basic rules Natural on a come-out throw: player wins Craps on a come-out throw: player loses ( craps out ) Point on a come-out throw: the player must keep throwing to get the same number before 7 appears to win ( make the point ), otherwise sevens out” Probability of winning: 49.29% 11

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Random experiments Playing craps is a random experiment: the outcome is not known before one throws the dice • Random experiment : is a procedure whose outcome is uncertain and cannot be predicted in advance Know what are possible outcomes 12
Sample space • Sample space : the set of all possible outcomes of a random experiment Sample space for come-out throw: S={(1,1),(1,2),(2,1),…,(6,6)} 36 possible combinations 13

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Sample space for come-out throw Craps 2 (1,1) Craps 3 (1,2),(2,1) Point 4 (1,3),(2,2),(3,1) 5 (1,4),(2,3),(3,2),(4,1) 6 (1,5),(2,4),(3,3),(4,2),(5,1) Natural 7 (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) 8 (2,6),(3,5),(4,4),(5,3),(6,2) 9 (3,6),(4,5),(5,4),(6,3) 10 (4,6),(5,5),(6,4) Natural 11 (5,6),(6,5) Craps 12 (6,6) 14
In the above definition of the sample space for come-out throw: all outcomes are equally likely , each with probability 1/36

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chap2 - GE 331 Analytic methods for uncertainty IE 300...

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