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Extra info for A case study in non-centering for data augmentation: Stochastic epidemics
What is the probability that a component is a resistor (either good or bad)? 11) to write 2. You have no use for either defective parts or resistors. What is the probability that a part is either defective and/or a resistor? 9) and the previous result we can write 3. What is the probability that a part is useful to you? Let U represent the event that the part is useful. 6)) 4. What is the probability of a bad diode? Observe that the events R, C, and G form a partition, since a component has to be one and only one type of part.
A number of examples and applications of the theory are discussed in this chapter. These are important to see how the theory applies in specific situations. The applications also illustrate some well-established models, such as the binary communication channel, which are important to electrical and computer engineering. Drake. Fundamentals of Applied Probability Theory. McGraw-Hill, New York,1967. Shannon. A mathematical theory of communication. Bell System Technical Journal, 27(3):379–422, July 1948.
Rudy has determined that the mission’s success or failure depends on only three major systems. Further, Rudy decides that the mission is a failure if and only if two or more of the major systems fail. The following is known about these systems. 1 and does not depend on the other systems. 5 if at least one other system fails. 1. 5 if the generator system fails. Otherwise the beer cooler cannot fail. (a) Draw the event space (sample space) for this problem by constructing a tree of possible events involving failure or nonfailure of the major systems.