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5. Random Processes
5. Random Processes

... A random process is a collection of time functions and an associated probability description. When a continuous or discrete or mixed process in time/space can be describe mathematically as a function containing one or more random variables. The entire collection of possible time functions is an ense ...
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A Review on `Probability and Stochastic Processes`

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... Probability that the next ball will also be orange Probability of selecting an orange ball from the original 15 Probability of selecting a white ball from the original 15 Correct ...
Multivariate z-estimators for location and scatter
Multivariate z-estimators for location and scatter

... magnitude of C (see Remark 2.1). Together with the boundedness condition in (R2), i.e., ak = sup pk < XI, this provides the good breakdown properties of the 7-estimators. To guarantee the existence of solutions of (Tp), the constant bl in (2.2) must be chosen such that 0 < bl < al. A typical functio ...
A Philosopher`s Guide to Probability
A Philosopher`s Guide to Probability

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... number of customers in the system has a Poisson distribution with mean and variance equal to r. The optimal number of agents required should be close to the mean number in this system plus some constant x times its standard deviation, which is C = r + x √r. A well-designed system should only have pe ...
Representing Variable Source Credibility in Intelligence Analysis
Representing Variable Source Credibility in Intelligence Analysis

... express dependencies between variables in a modelled domain. The graphs are easily readable and intuitive for humans and at the same time are convenient and efficient tools from an algorithmic perspective. In graphical models, variables are represented by nodes in the graph and dependencies between ...
Bayesianism with a Human Face - Minnesota Center for Philosophy
Bayesianism with a Human Face - Minnesota Center for Philosophy

Ideology and existence of 50%-majority equilibria in multidimensional spatial voting models ∗
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... constitutional treaty during the Spring of 2005, one cannot explain the cleavages between and within parties through the traditional left-right dimension. One also needs the now classical ideological dimension ‘sovereignist-federalist’ to explain the split of the gaullist party; furthermore the pos ...
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... in a train strike (A) then this in turn will increase our belief in both Martin being late (B) and Norman being late (C). Of more interest is whether information about B can be transmitted to C (and vice versa). Suppose we have no hard evidence about A (that is, we do not know for certain whether or ...
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Reflections on Fourteen Cryptic Issues Concerning the Nature

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... randomly chosen point falls on a particular meridian). We should pass to the limit only after absorbing the new information’ 1.3. Measure-theoretic probability before the Grundbegriffe. 1.3.1. The invention of measure theory by Borel and Lebesgue. Borel is considered the father of measure theory. Hi ...
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Probability box



A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.
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