Collectively exhaustive

B. Stenbom, M. Luna, J. C. Saenz, J. SantamarPlatinum-group elements quantisation in collected exhaust fumes and studies of catalyst surfaces, Sci. Total Environ., 257 (2000), ID 15. 

Paiacios MA, Gomez MM, Moldovan M, Mor-EisoN G, Rauch S, McLeod C, Li R, Laserna J, Lucena P, Caeoli S, Alimonti A, Schramel P, Lustig S, Wass U, Stenbom B, Luna M, Saenz JC, Santamaria J and Torrents JM (2000) Platinum-group elements quantification in collected exhaust fumes and studies of catalyst surfaces. Sci Total Environ 207 1-15. 

For the lead trap cars, lead emissions were only one-third those of the standard cars over the urban cycle and one-twelfth those of the standard cars over the highway cycle. This test demonstrates that purging of previously collected exhaust particulate matter does not take place with properly designed traps when switching from sustained mild driving conditions to more severe conditions of continuous operation at highway speeds. 

Modern theory is often called Bayesian probability theory after Thomas Bayes, F.R.S. (1702-1761) who was a minister of the Presbyterian church. The theorem attributed to his name is central to the modern interpretation, but according to Maistrov, it appears nowhere in his writings, and was first mentioned by Laplace though it was only expressed in words. The theorem enables an updating of a probability estimate, in the light of new information. For a set of mutually exclusive collectively exhaustive events Bi, B. ., B then P A) can be expressed. Fig. 5.4, as... 

Furthermore, the model set expansion approach is based on two fundamental assumptions mutual exclusiveness and collective exhaustiveness of the set of models. While the first assumption can be often accepted in practice, excluding the case in which one of the model is a special case of another model, the second is often not met in practice because it requires that a perfect model not only exists but that it also be one of the n models considered. In general, the complexity of the phenomena is such that the list of plausible models considered is necessarily incomplete. 

Collectively Exhaustive. Outcomes Ai,A2,...,Af are collectively exhaustive if thev constitute the entire set of possibilities, and no other outcomes are possible. For example, [heads, tails] is a collectively exhaustive set of outcomes for a coin toss, provTded that you don t count the occasions when the coin lands on its edge. 

EXAMPLE 1.10 A gambling equation. Suppose you have a collection of mutually exclusive and collectively exhaustive events E, with probabilities... 

A property of probability distribution functions is that the sum of the probabilities equals one. Because the outcomes are mutually exclusive and collectively exhaustive, Equations (1.3) and (1.5) apply and... 

This set of composite events is mutually exclusive and collectively exhaustive. 

Here and in later chapters we use lattice models. In lattice models, atoms or parts of molecules are represented as hard spherical beads. Space is divided up into bead-sized boxes, called lattice sites, which are artificial, mutually exclusive, and collectively exhaustive units of space. Each lattice site holds either zero or one bead. Two or more beads cannot occupy the same site. The lattice model just captures the idea that particles can be located at different positions in space, and that no two particles can be in the same place at the same time. This is really all we need for some problems, such as the following. 

Mutually exclusive and collectively exhaustive (MECE) damage states. A damaged component can be in one and only one damage state. Order does not matter. 

Equation 4 indicates that probability measures are positive numbers, and as indicated by the third axiom (Pro3), a basic property of probability measures is that they are additive. This requirement is commonly referred to as the additivity requirement. This requirement ensures the sum of probabilities over any collectively exhaustive, mutually exclusive set of events is equal to 1 (unity). Considering a single event A, and its complement denoted A, from (Eq. 4) it can be shown that... 

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