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6.262.PS5

# 6.262.PS5 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.262 – Discrete Stochastic Processes Problem Set #5 Issued: March 5, 2010 Due: March 12, 2010 Reading: For this week, read sections 3.1 – 3.4 of Chapter 3 in the course notes. For next week, read sections 3.5 and 3.6. 1) Exercise 3.4 from the course notes. 2) Exercise 3.11 from the course notes. 3) Exercise 3.12 from the course notes. 4) Exercise 3.16 from the course notes. Briefly explain your reasoning for parts a), c) and d). 5) Exercise 3.20 from the course notes. In part (b), the “zero-th” arrival is not counted as one of the even arrivals. Please sketch the function i ( ) ( ) m t E N = you find in part c) and explain its shape. 6) To construct the sequence of random variables Y 1 , Y 2 , Y 3 , ---, first choose a single number ω from the uniform distribution on the open unit interval (0,1). Then assign each Y n , n = 1, 2, --- the value n, 0 < 1/n ( ) 0, > 1/n n Y ω ω ω = a) Sketch Yn( ω ) as a function of ω for n = 1, 2 and 3.

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6.262.PS5 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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