September_27th_Lecture_3000

September_27th_Lecture_3000 - September 27th Lecture CEE...

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September 27 th Lecture CEE 3000 Incorporating Uncertainty in System Analysis Axioms (fundamentals of probability theory) Simple calculations to characterize the uncertainty in systems Probability – likelihood of an event accruing relative to the set of all possible events. 1. Sample Space- set of all possible events {all possible events} 0 =< P(E1) =< 1 P(s) = 1 s= sample space assumptions 1. discrete random events 2. equally likely outcomes Sdie = {1 2 3 4 5 6} ^ ^ Unbiased discrete random events P(1) = P(2) = …P(6) = 1/6 P(odd) = P(1) + P(3) + P(5)= 3/6 ½ P(even) = P(2) + P(4) + P(6) = 3/6 ½ *we can add bc they are mutually exclusive 2. Mutually Exclusive Events Events that cannot happen at the same time E1∩E2 = Ø P(E1∩E2) = Ø even P(E1 or E2) P(E1UE2) = P(E1) + P(E2) P(Ø) = 0 3. Overlapping Events Events that can occur simultaneously E.g. Flip a coin and a die at the same time Die Coin H T 1 H T 2 2H 2T 3 3H 3T
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4 4H 4T 5 5H 5T 6 6H 6T P(E1UE2) = P(E1) + P(E2) – P(E1∩E2)
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September_27th_Lecture_3000 - September 27th Lecture CEE...

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