ENMA 420-520 Lecture 3 Slides

ENMA 420-520 Lecture 3 Slides - Statistical Concepts for...

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Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #3 Discrete Random Variables 11
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10/17/09 Basic Definitions Random Variable: A numerical-valued function defined over a sample space. Each simple event in the sample space is assigned a value of Y. Discrete Random Variable: One that can only assume a countable number of values. Binary state: {0, 1} 22
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10/17/09 Probability Distribution A table, graph or formula that gives the probability p(y) associated with each possible value of Y = y. Example: For Y = {H, T}, may have p(H) = 0.5, p(T) = 0.5 Requirements: 0 <= p(y) < = 1 33
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10/17/09 Exercise 4.4 a. The list of all possible pairs of beach hotspots is shown at right: b. The probabilities of each of these outcomes should all be equal if a random sampling Beach Hotspot Pair MBF CINY MBF SCA MBF MBNJ MBF OCNJ MBF SLNJ CINY SCA CINY MBNJ CINY OCNJ CINY SLNJ SCA MBNJ SCA OCNJ SCA SLNJ MBNJ OCNJ MBNJ SLNJ OCNJ SLNJ
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10/17/09 Exercise 4.4 (Cont’d) c. The value of Y is found by determining the total number of beach hotspots in the sample with a planar nearshore bar condition. Beach Hotspot Pair P(Sample ) Y MBF CINY 1/15 0 MBF SCA 1/15 0 MBF MBNJ 1/15 1 MBF OCNJ 1/15 0 MBF SLNJ 1/15 1 CINY SCA 1/15 0 CINY MBNJ 1/15 1 CINY OCNJ 1/15 0 CINY SLNJ 1/15 1 SCA MBNJ 1/15 1 SCA OCNJ 1/15 0 SCA SLNJ 1/15 1 MBNJ OCNJ 1/15 1 MBNJ SLNJ 1/15 2 OCNJ SLNJ 1/15 1
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10/17/09 Exercise 4.4 (Cont’d) d. The probability distribution for Y is found by grouping similar values of Y together in the table. Y = y P(Y) 0 6/15 1 8/15 2 1/15 e. P(Y ≥ 1) = P(1) + P(2) = 8/15 + 66 0 2 4 6 8 10 12 P(Y)
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10/17/09 Exercise 4-8 77 0 2 4 6 8 10 12
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10/17/09 5 Minute Break Assignment: Discuss examples of discrete random variables Discuss some random variables that would not be discrete 88
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This note was uploaded on 10/17/2009 for the course MET 387 taught by Professor Dean during the Spring '09 term at Old Dominion.

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ENMA 420-520 Lecture 3 Slides - Statistical Concepts for...

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