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In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. A probability matrix is a matrix used to describe the transitions of a Markov chain. A Markov chain is a mathematical system that undergoes transitions from one state to another, among a discrete (finite or countable) number of possible states. Many events are influenced by previous occurrences or events. Therefore, certain outcomes tend to have specific consequences, even though the occurrence of those outcomes is random. This idea of the chain of arbitrary results with a weighted likelihood of occurrence is Markov chain analysis. Simply said, it is he stream of events and how they are connected to each other. The model being used in this question is not an example of a Markov chain.
The value (1 - P) is not a measure of the seriousness of the consequences. There is no such measure.
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. A probability matrix is a matrix used to describe the transitions of a Markov chain. A Markov chain is a mathematical system that undergoes transitions from one state to another, among a discrete (finite or countable) number of possible states. Many events are influenced by previous occurrences or events. Therefore, certain outcomes tend to have specific consequences, even though the occurrence of those outcomes is random. This idea of the chain of arbitrary results with a weighted likelihood of occurrence is Markov chain analysis. Simply said, it is he stream of events and how they are connected to each other. The model being used in this question is not an example of a Markov chain.
If P represents the probability that the process is in control , then (1 ? P) must represent the probability that the process is out of control . The problem tells us that the model is a two-state model. The process can be either in control or out of control, and there can't be any other probabilities. The sum of all probabilities is always equal to 1. Therefore, when P is the probability that the process is in control, (1 ? P) must be the probability that it is out of control. Furthermore, L stands for the cost if the process is out of control, and C stands for the cost of correction if the process is out of control. We find the expected cost of an event by multiplying its cost by the probability that the event will occur. Since L and C are both multiplied by (1 ? P), (1 ? P) must stand for the probability that the process is out of control.