Download e-book for kindle: Ecole d'Ete de Probabilites de Saint-Flour XI - 1981(s) by X. Fernique, P. W. Millar, D. W. Stroock, M. Weber, P. L.

By X. Fernique, P. W. Millar, D. W. Stroock, M. Weber, P. L. Hennequin

ISBN-10: 3540119876

ISBN-13: 9783540119876

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Extra resources for Ecole d'Ete de Probabilites de Saint-Flour XI - 1981(s)

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Frequency of ﬁres. g. Ramachandran [65]. We turn now to two examples of streams to which we will return on several occasions. 6. Consider alarm systems for ﬂoods. A warning is issued if the water level at some measuring station exceeds a critical threshold ucrt . Now, with A = “Warning for ﬂood is issued”, and t one year, the yearly probability of ﬂood warnings Pt (A) is the frequency of years in which at least one warning was issued. Actually the probability is also equal to P(“Maximal water level during one year exceeds ucrt ”); the last chapter will be devoted to computations of this probability.

Assume now that a person has been tested positively for the disease. Use Bayes’ formula to compute the probability that the person is really infected. 8. 10, leakage of containers. 002 year−1 The prior odds for the three conditions water ﬂow, chemical interactions, and others are 4:1:95. Assume that the conditions are mutually excluding, one and only one of them is true. The cost diﬀers depending on scenario, hence it is of interest to update the probability distributions based on available information.

2. Let A1 , A2 , . . e. P(Aj )/P(Ai ) = qj /qi . Then P(Ai ) = ✧ qi . 1. Consider an urn with balls of three colours. 50 % of the balls are red, 30 % black, and the remaining balls green. The experiment is to draw a ball from the urn. Clearly A1 , A2 , and A3 , deﬁned as the ball being red, black, or green, respectively, forms a partition. It is easy to see that the 24 2 Probabilities in Risk Analysis odds for Ai are 5:3:2. 3. 5+3+2 We now present Bayes’ formula for odds. Consider again any two statements Ai and Aj having odds qi : qj , which we call a priori odds and also denote as qiprior : qjprior .