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Fundamentals of Probability with Stochastic Processes
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Stochastic Processes Problems and Solutions
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Suppose that your policy when arriving at the bus stop is to wait up to a time s, and if a bus has not yet arrived by that time then you walk home. Find the expected time that the person waits before starting to cross. From Proposition 2. Similar to the proof of Proposition 2.
Topics in Stochastic Processes
Each arrival independently makes its way through the states of the system. As shown in Problem 2. And the later part is equal to the expectation of the amount of time an individual is in state i during its first t units in the system. Thus the increments are independent. From Corollary 2.