1 / 20

Formal analysis of uncertainties and probability

Not all problems can be solved by analysis of data Set Theory Sample space : collection of all possibilities Sample point : each possibility Event : subset of sample space Probability Theory. Formal analysis of uncertainties and probability. Constructions job needs 3 bulldozers

galena
Download Presentation

Formal analysis of uncertainties and probability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Not all problems can be solved by analysis of data Set Theory Sample space: collection of all possibilities Sample point: each possibility Event: subset of sample space Probability Theory Formal analysis of uncertainties and probability

  2. Constructions job needs 3 bulldozers • Each bulldozer could be operative or not operative after 6 months • We are interested in the operative status of the 3 bulldozers

  3. E – at least 2 bulldozers operative E1 – operator #1 no job

  4. 1,2 3,4,5 1 2 9 Travel Time Total travel time T: {4,5,6,7} Suppose 1,2 are equally likely Suppose 3,4,5 are equally likely P (T=5) =?

  5. 2 9 2 1 Assume statistical independence

  6. P (1) = 2/3 P (2) = 1/3 P (3) = ¼ P (4) = ¼ P (5) = 1/2 P (T=5) = 2/12+1/12 = 1/4

  7. 1 Km Number of crack on a highway S = {0,1,2,……….∞} discrete

  8. 100 ton B A RA RB Continuous S E RA : 0-100 RA 0 90 100

  9. S: for load=100

  10. Union: either E1 or E2 occur E1∪E2 Intersection: both E1 and E2 occurE1∩ E2 or E1 E2

  11. E1 = road 1 closed E2 = road 2 closed 1 2 1 E3 = road 3 closed A C B 3 2 Examples B A No communication between A and B = E1E2 No communication between A and B = E3∪E1E2

  12. E1 = river 1 floods E2 = river 2 floods 1 2 Town Flood in town = E1∪E2

  13. E1 = 1 settles Ē1 = 1 does not settle E2 = 2 settles Ē2 = 2 does not settle 2 1 Example - pair of footings Settlement occurs = E1∪E2 Tilting occurs = E1Ē2∪Ē1E2

  14. Mutually exclusive m.e. E1 and E2 are m.e. if occurrence of one precludes the occurrence of the other S E1 E2

  15. Examples of m.e. events • Zero and 1 quakes in a year • E1 and Ē1 • E1 and E2 in the footing example?! • E1 Ē2 and Ē1E2 in the footing examples?!

  16. Collectively exhaustive c.e. A set of events are c.e. if the union makes up the sample space

  17. E 2.7 Contractors A and B bidding for jobs (1) bidding for different jobs (2) bidding for same job A B A B

  18. A B (3) A, B are the only bidders (4) B is a subcontractor of A only – also there are other bidders beside A A B

  19. Operating rules AB = BA A∪B = B∪A (A∪B)C = AC ∪ BC

  20. B (A∪B)(B∪C) = AB∪AC∪BB∪BC = AB∪AC∪B = AB∪B∪AC = B∪AC B C B Algebra: (a+b) (b+c) = ab+ac+b2+bc ≠b+ac

More Related