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Chapter 2

# Chapter 2 - IENG 213 Probability and Statistics for...

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Click to edit Master subtitle style IENG 213: Probability and Statistics for Engineers Instructor: Steven E. Guffey, PhD, CIH © 2002-2009 Chapter 2: Probability

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22 Background Concerned with presentation and interpretation of chance outcomes
33 Background Observations: any recording of data Counts or measurements E.g., Number of potential voters who voted for one candidate E.g., Heights of children with leukemia Categorical: value assigned by classification by some criteria E.g., Attitudes of children watching violent shows

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44 Background Experiment: any process that generates data E.g., counting cars that run a red light E.g., measuring height of corn in fields treated with different herbicides Ideally, have many observations Usually outcome that is not pre-determined Cannot be predicted (that’s why we do the experiment) Depends on chance
55 Sample Space Definition 2.1: Set of all possible outcomes of a statistical experiment Element: individual outcome within the sample space. Also called “member” or “sample point” or “data point” S, symbol for sample space: E.g., flipping coin S = {No. Heads, No. Tails} E.g., tossing a die S = {1, 2, 3, 4, 5, 6} E.g., grades on a statistics course S = {A, B, C, D, F, I, W}

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66 More than one sample space can be used to describe the results of an experiment Consider the sample space of a die: If interested in the side that shows up: S1 = {1, 2, 3, 4, 5, 6} If interested only in whether odd or even: S2 = {even, odd} If interested in how often 6 comes up: S3 = {<6, 6}
77 Tree Diagram Method of depicting all possible outcomes in an experiment Example: number of students making an A on second exam who made an A on the first exam S = {AA, A < A , < A A , < A < A} First outcome A B, C, etc. Second outcome A B, C, etc. A B, C, etc. Sample point A, <A A, A <A, <A <A, A

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88 Sample rules For large or infinite sample spaces, convenient to define sample space by rules E.g., heights of NBA players S = {ht | ht < 7 ft} E.g., points on a circle S = {(x,y) | x2 + y2 = 4 } x y
9 2.2 Events E.g., values on the top, right hand quadrant of a circle: Event: subset of a sample space May be interested in one specific outcome B = {(x,y) | x2 + y2 = 4 }, where x>0 and y>0} S = {(x,y) | x2 + y2 = 4 } x y x y

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10 2.2 More Events S = {(x,y) | x2 + y2 < 4 } B = {(x,y) | x2 + y2 < 4 }, where x>0 and y>0} x y x y
11 Null Set, Complement Event Null set is the ________ Example: MAE Courses = {thermo, statics, fluids, solids} Easy courses = {NBW 101, PHI 103, SOC 101} B = courses that are both MAE and Easy = { ø } Complement: all other items ____ in an event E.g., S = {1,2,3,4,5,6} A = {1,2,3} B = A’ = {4,5,6}

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1212 Overlapping Events or Subsets Intersection of two events, A and B Example: A = {a,b,c} B = {b,c,d,e,f} Logic: elements in A and B
1313 Disjoint Subsets Mutual exclusive (disjoint), A and B no elements in common Example, A = {a,b,c} B = {d,e,f} Logic: elements in A and B

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Chapter 2 - IENG 213 Probability and Statistics for...

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