Download Decisions under uncertainty : probabilistic analysis for by Ian Jordaan PDF

By Ian Jordaan

1. Uncertainty and decision-making -- 2. the idea that of likelihood -- three. Distributions and expectation -- four. the idea that of software -- five. video games and optimization -- 6. Entropy -- 7. Mathematical facets -- eight. Exchangeability and inference -- nine. Extremes -- 10. probability, protection and reliability -- eleven. facts and simulation -- 12. end

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Extra info for Decisions under uncertainty : probabilistic analysis for engineering decisions

Sample text

In doing this, you should take into account all available information. The extent to which we search for new information and the depth to which we research the problem of interest will vary, depending on its importance, the time available and generally on our judgement and common sense. We have some knowledge of the concrete delivered previously, of a similar specified grade. To be precise: we cast a cylindrical specimen of the concrete, 15 cm in diameter and 30 cm long (6 by 12 inches) by convention in North America.

The quantity X is what is normally termed a ‘random variable’, implying that it varies; this is incorrect. X does not vary; it will take on a particular value, which we do not know. That is why we need probability theory. We shall therefore adopt the term ‘random quantity’ as suggested by de Finetti rather than ‘random variable’. As noted, ‘random’ is retained with the understanding that the meaning is taken as being close to that of the phrase ‘whose value is uncertain’. Bruno de Finetti used the word ‘prevision’ for what would usually be described as the mean or expected value of a quantity, but with much more significance.

10) for any incompatible events E i , E i+1 , . . , E j . These results all follow from coherence, and de Finetti has shown that we can extend the idea in a very simple way. Suppose that we have the following linear relationship between the events {E 1 , E 2 , . . , E n }, which do not need to be incompatible: a1 E 1 + a2 E 2 + · · · + an E n = a. 11) This relationship holds no matter which of the E i turn out to be true; an example is the equation E i = 1 above for the special case of partitions.