Of disjoint events

In calculating P(k) we simply sum the probabilities of the ( ) disjoint events, each of which has the same probability P/fc). 

When the two events SI and B are not disjoint, i.e., when the occurrence of one event does not exclude the occurrence of the other, we have the relation... 

Consider, for example, two disjoint events, A and B, defined in terms of adjoining intervals of real numbers, as shown in Figure 5a. Due to the effect of measurement errors, observations at the sharp boundary between events A and B are totally meaningless and should be completely discounted. Moreover, observations in the close neighborhood of this boundary (within the reach of measurement errors) are not fully credible and should be discounted according to some discount-rate function, as illustrated in Fig. 5a. When the same measurements are taken for the union A JB, as shown in Fig. 5b, the discount-rate function is not applicable. Hence, the same observations produce more evidence for the single event A JB than for the two disjoint events A and B. The evidential support for y4 U B is thus not equal to the sum of the evidential supports for A and B. That is, the additivity requirement of probability measures is violated the correct measure is in this case superadditive. Alternatively, an appropriate granulation can be used to define probabilities on fuzzy events. ... 

I must point out that we conceive the process of innovation as really being a non-process but rather being a series of rather disjointed events which began with ideation, then followed by... 

It is at this point that care must be exercised in writing the probability of the event on the lhs of (2.15). In general, there exists no simple relation between the probability of a union of events and the probabilities of the individual events. However, if we choose dR to be small enough so that no more than a single particle may be found in dR at any given time, then all the events listed above become disjoint (i.e., occurrence of one event precludes the possibility of simultaneous occurrence of any other event). In this... 

This interpretation follows from the fact that the events particle 1 in dR1 and particle 1 in dR" are disjoint events (i.e., a specific particle cannot be in two different elements dR1 and dR simultaneously). Hence, the probability of the union is obtained as the sum (or integral) of the probabilities of the individual events. 

To summarize, the alphabet of scheduling events A is the disjoint sum of alphabets A which deal with scheduling events concerning particular disjoint sets of signals Si. The alphabet A is associated with Pi in the sense that Si is exactly the set of signals scheduled by P,-. 

Following the IMO resolution (1997), five categories of ICF event consequences are distinguished. Their description is given in Table 1. They are divided into accidents and incidents. Occurrence of a consequence of specific category is an event. The set of events in the version presented in Table 1 is a complete system consisting of disjoint repertory consequences. 

Semantically, an event composition automaton only observes event occurrences of the given role automata. Consequently, only those events can be used in an event composition automaton, as others can never be observed. Additionally, the set of clocks of the event composition automaton is restricted to be disjoint to the set of clocks of the role automata. This way, it is guaranteed that the event composition automaton cannot widen the time intervals of event sequences of the automata to be synchronized. This in turn guarantees that all verified deadlines of the role automata can still be met and, therefore, that all verified safety properties of the role automata are preserved (see section 6). 

In (2.8.42), the sum is over all states that are consistent with the presence of a cavity in the system. In (2.8.43), the sum is over all possible states of the system. Since the probability of finding any particular state j is exp( - j3 y)/2ad, the probability of finding a cavity is the sum over the probabilities of all the (disjoint) events consistent with the requirement that such a cavity exists,... 

Exclusive OR Gate Only one of the inputs can occur, not both. Disjoint events. D a D... 

Equivalently, if the point process is regular, the nth degree product density function/ (ti,..., t ) represents the probability that one event occurs in each of disjoint intervals [t t, -i-irrespective of other events in the interval [0, t] thus,... 

The two events the system is in state L and the system is singly occupied are clearly not disjoint. The occurrence of one does not exclude the occurrence of the other. In order to construct the probability of the sum of these two events, we need the following three ingredients ... 

Let me examine now the nature of mathematical models that involve probability. Due to the additivity requirement of probability theory, elementary events are required to be pairwise disjoint and the probability of each is required to be expressed by a real number. The requirement of... 

The traditional system of providing patient care— wherein physicians initiate drug therapy, pharmacists dispense medications, and nurses administer medica-tion.s—is often run in a disjointed fashion. This results in potentially avoidable adverse drug events that contribute to poor patient outcomes and increased medical costs. Efforts aimed at modifying the current processes of care to enhance efficiency of workflow, improve patient outcomes, and reduce medication errors arc needed. 

When it comes to assigning probabilities to events, the procedure arises from the idea of assigning areas to sets. This idea can be conveyed by pictures called Venn diagrams. For example, consider the disjoint sets of events A and B in the Venn diagram of Fig. 21.2. 

In this formulation by density functions and (Riemann) integrals, the basic events are the intervals [a,b] and countable unions of these disjoint intervals. It is easy to see that this approach satisfies aU of the axioms for a probability space listed earlier. This formulation lets us apply aU of the techniques of calculus and analysis to probability. This feature is demonstrated repeatedly in the sections to follow. 

Since the ligands are also equivalent, the probabilities P (/th) are also independent of the index k. In addition, the N events particle k occupies a specific site are disjoint... 

---