IE_111_-_ch02_-_supplemental_slides-3

# IE_111_-_ch02_-_supplemental_slides-3 - Chapter 2:...

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Chapter 2: Probability Supplemental slides

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A random experiment : An experiment that can result in different outcomes, even though it is repeated in the same manner every time.
V = I R (is it?)

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Sample Space Continuous S = R + = { x| x >0 } unbound S = R + = { x| 10 x 11 } bound ≤ ≤ Discrete S = { yes, no } S = { low, med, high }
An EVENT is any SUBSET OF “S” Events are used to define outcomes of interest The description of the events determines “S” Example 2-1 from Text Thickness of molded plastic parts Continuous S = R + = { x| x >0 } thickness is always positive, no assumptions S = R + = { x| 10 x 11 } ≤ ≤ thickness known to be in this range Discrete S = { yes, no } conforms to specifications S = { low, med, high } specs for low, med and high are

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fig_02_05 Example 2-3 Digital communications system, messages can be on-time or late. 3 messages are classified as a sample. There are 8 outcomes. Sample space can be described graphically with tree diagram S = { (ot-ot-ot), (ot-ot-lt), (ot-lt-ot), (ot-lt,lt), (lt-ot-ot), (lt-ot-lt), (lt-lt-ot), (lt-lt-lt) }
fig_02_06 Example 2-4 Automobile configurations available are: with or w/o Automatic transmission (a, m) . . 2 choices with or w/o A/C (w,wo) 2 choices 3 types of stereo (s1,s2,s3) 3 choices Ext. color (rd,wh,bl,br) 4 choices How many elements are there in S? S = { (a,w,s1,rd), (a,w,s1,wh), ……., (m,wo,s3,bl), (m,wo,s3,br) } Multiplication rule (pg 25) S has 48 elements (2 X 2 X 3 X 4)

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fig_02_07 Example 2-5 Automobile configurations Further definition of the problem to limit interior color choices based on the exterior color choice
Events New Events can be described in terms of existing ones Union - All outcomes contained in E1 and E2 Intersection - All events in BOTH E1 and E2 Complement – All events in “S” but NOT in E

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Venn Diagrams
Mutually Exclusive Events in “S”

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( 29 A B A B = ( 29 A A B A = ( 29 ( 29 A B A B A = ( 29 ( 29 ( 29 A B A B A B A B = ( 29 ( 29 ( 29 A B C A B A C = Verify the following set theory identities using Venn diagrams: A B
Example 2 An experiment consists of throwing a pair of dice, one yellow and the other blue. If x is the number showing on the yellow die, and y is the number showing on the blue die, then an outcome can be represented as (x,y). List the elements of event A: the sum of the two numbers is greater than 8. (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6,4) (6,5) (6,6) List the elements of event B: a 3 occurs on either of the two dice. (1,3) (2,3) (3,3)(4,3)(5,3)(6,3) (3,1) (3,2) (3,4) (3,5) (3,6) List the elements of event C: A number greater than 4 occurs on the blue die. (1,5) (1,6) (2,5) (2,6) (3,5) (3,6) (4,5) (4,6) (5,5) (5,6) (6,5) (6,6)

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## This note was uploaded on 02/07/2011 for the course IE 111 taught by Professor Storer during the Spring '07 term at Lehigh University .

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IE_111_-_ch02_-_supplemental_slides-3 - Chapter 2:...

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