Sysen531
Final Exam
1. A professor continually gives exams to her students. The exams are of three types and her students are graded as having done well or badly. Let pi denote the probability that they do well on a type i exam and suppose that p1=0.3, p2=0.6 and p3 =0.9. If the class does well on an exam then the next exam is equally likely to be any one of the three types. If the class does badly then the next exam is always type 1.
1) Use a markov chain to determine the long term proportion of the exams of the three types.
2) If the first exam is type 1 what is the mean number of exams until the class is first given an exam of type 3
2. There are five cards in a set. A bubble gum card purchaser will receive one card equally likely to be any one of the five. Let
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3) Compute L and W when there is no capacity restriction. 4. The schematic below represents a client/server system in which M clients independently of each other send jobs to a server where they wait for processing. The time between requests is the same for all clients and is exponentially distributed with a mean of 100 ms. The processing time at the server is exponential with a mean of 20 ms. Using the appropriate queuing model, compute the server utilization (probability that the server is busy) and the waiting time W (known as the response time in this application), as the number of clients M varies from 1 to 20. (Use a data table). Plot W against M to show the effect of the number of clients on the system response. At high server utilization the system is congested and each additional client increases the response time by its service time and the plot of W against M becomes linear. From your computed results calculate the change in W as M increases from 19 to 20. 5. The sketch below shows the trajectory of a projectile propelled with an initial velocity V0 at an angle 8. Neglecting air resistance the horizontal range travelled is given

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