By Aleksander Janicki

Provides new laptop equipment in approximation, simulation, and visualization for a bunch of alpha-stable stochastic procedures.

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Thus, in modeling a communication system, the effect of noise must be taken into consideration. Since channel noise is a random phenomenon, one of the performance issues is the probability that a received message is not corrupted by noise. Thus, probability plays an important role in evaluating the performance of noisy communication channels. 5 System Simulation Sometimes it is difficult to provide an exact solution of physical problems involving random phenomena. The difficulty arises from the fact that such problems are very complex, which is the case, for example, when a system has unusual properties.

Thus, if the cardinality of the set A is n, then the cardinality of the power set of A is |s(A)| ¼ 2n. 3 Venn Diagram The different set operations discussed in the previous section can be graphically represented by the Venn diagram. 3 Venn Diagrams of Different Set Operations union, intersection, and difference operations on two sets A and B. The universal set is represented by the set of points inside a rectangle. The sets A and B are represented by the sets of points inside oval objects. 4 Set Identities The operations of forming unions, intersections and complements of sets obey certain rules similar to the rules of algebra.

Thus, the probability that the target is hit at least once is the probability of the union of its being hit once and its being hit twice. 9 COMBINED EXPERIMENTS Up till now our discussion has been limited to single experiments. Sometimes we are required to form an experiment by combining multiple individual experiments. Consider the case of two experiments in which one experiment has the sample space Ω1 with N sample points and the other has the sample space Ω2 with the M sample points. That is, Ω1 ¼ fx1 , x2 , ..