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# Lecture4 - Risk Assessment and Management Lecture 4...

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1 Risk Assessment and Management Lecture 4: Analytical Tools Used in Risk Assessment- Poisson Models Reading Material of the Week s Ingleton, Natural Disaster Management (From Reading Materials) s Benjamin and Cornell, Probability Statistics and Decision for Civil Engineers (From Reading Materials) s Three Mile Island (Will Be Provided in The Lecture)

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2 Learning Objectives s Be able to conceptualize independent accident and arrival problems as a Poisson Process . s Answer questions related to the probability of different numbers of arrivals and the time between arrivals using Poisson distribution and the Gamma distribution. s Similarly, students should be able to explain difference between the frequency of arrivals and the probability of an arrival and compute one from the other. Review of Probability s Experiment – any process or procedure for which more than one outcome is possible s Sample Space – the collection of all possible outcomes s Event – Any subset of the sample space (i.e., the price of a stock increasing, a rainy day, the outcome 5 in one toss of a die) s Complements of Events – Complement of event A is the event consisting of everything in the sample space that is not contained within the event A. s Probability – the chance (possibility) that an uncertain event will occur (always between 0 and 1; 0: the impossible event, 1: the certain event)
3 Review of Probability The Sample Space is the collection of all possible events e.g. All 6 faces of a die: e.g. All 52 cards of a bridge deck: Review of Probability s Simple event s An outcome from a sample space with one characteristic s e.g., A red card from a deck of cards s Complement of an event A (denoted A ) s All outcomes that are not part of event A s e.g., All cards that are not diamonds s Joint event s Involves two or more characteristics simultaneously s e.g., An ace (A) that is also red from a deck of cards

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4 Review of Probability -Example (a) What is the sample space when a coin is tossed two times? (b) What is the probability of getting two heads? (c) What is the probability of getting at least one head? Review of Probability s Mutually exclusive events s Events that cannot occur together s example: A = queen of diamonds; B = queen of hearts s Events A and B are mutually exclusive
5 Review of Probability s Collectively exhaustive events s One of the events must occur s The set of events covers the entire sample space example: A = aces; B = black cards; C = diamonds; D = hearts s Events A, B, C and D are collectively exhaustive (but not mutually exclusive – an ace may also be a heart) s Events B, C and D are collectively exhaustive and also mutually exclusive Review of Probability s Probability is the numerical measure of the likelihood that an event will occur s The probability of any event must be between 0 and 1, inclusively s The sum of the probabilities of all mutually exclusive and collectively exhaustive events is 1 0 ≤ P(A) ≤ 1 For any event A 1 P(C) P(B) P(A) = + + If A, B, and C are mutually exclusive and collectively exhaustive Certain Impossible 0.5 1 0

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Lecture4 - Risk Assessment and Management Lecture 4...

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