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By Haym Benaroya; Seon Mi Han

ISBN-10: 0824723155

ISBN-13: 9780824723156

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The former will counter that it is often not possible to perform enough experiments to arrive at that rigorous probability and judgment must be used. Fortunately, our purposes here do not require us to resolve this debate. We can assume that in some manner it is possible to obtain the probabilities necessary for our computations, usually based on data analysis. 2 Think of a randomly vibrating oscillator where random behavior implies unpredictable periods, amplitudes, and frequencies. 7. As another example, what do you suppose is the temperature of the flame in a fire?

01 < ω2 , is a sample point whose occurrence is a realization. 1 Basic Events Several events are needed for a complete modeling framework. They are: 1. The impossible event, denoted by {} or φ, is the event with no sample null event is an empty point. In the sample space, the impossible or set. 2. The certain or universal event, denoted by S or Ω, is the event that contains all the sample points. The certain event is in fact the sample space itself. 3. The complementary event is denoted by the event symbol with an E, the complementary event is E, meaning that it contains all sample points in S that are not in E.

At this point a physical judgement is required about the joint event (seismic event, quantity of water in tank). It is reasonable to assume that these two events are statistically independent. 3. 5. While this is the answer to the problem, a designer would look at the results and think about how the probability of collapse can be reduced. The general equation for Pr(C ) shows how each component probability on the right hand side adds up to the total probability. It suggests weaknesses in the structure.

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Probability models in engineering and science by Haym Benaroya; Seon Mi Han


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