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6.262.PS6

# 6.262.PS6 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.262 – Discrete Stochastic Processes Problem Set #6 Issued: March 12, 2010 Due: March 19, 2010 Reading: Finish sections 3.5 and 3.6. Next week: Study Section 3.7 carefully and skim section 3.8. 1) Exercise 3.6 from the course notes. 2) Exercise 3.7 from the course notes. (Hint: The total reward Rn should be the expected number of customers turned away during the nth interrenewal period. The “expected reward function” R(t) should be a function with the property that b a [# customers turned away for a t b = ( ) . E R t dt ) 3) Exercise 3.14 from the course notes. 4) Exercise 3.24 from the course notes. (In part e), also check your answer in the special case that the bus arrivals are a Poisson process with rate μ .) 5) Exercise 3.28 from the course notes. 6) In this problem we use some properties of the Laplace transform to prove an elementary version of Blackwell's theorem. You may assume that f X (x) has a Laplace transform that is a rational

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