6.262.PS4

6.262.PS4 - 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 #4 Issued: February 26, 2010 Due: March 5, 2010 Reading: For this week, read Sections 1.1 – 1.5 of Chapter 4. (We will only use the results of the Perron - Frobenius Theory in Section 4.4, e.g., the statements of Theorems 4.6 – 4.8.) For next week, read Sects. 3.1 – 3.3 of Chapter 3. 1) Exercise 2.22 from the course notes. 2) Exercise 2.24 (parts a – d only) from the course notes. 3) Exercise 2.26 from the course notes. 4) Exercise 4.1 (part a only) from the course notes. 5) Exercise 4.6 from the course notes. 6) Exercise 4.7 from the course notes. Problem 7 (This is a slightly simpler version of Exercise 4.25 in the course notes.) Consider a sequence of IID binary random variables with 12 ,, XX " { } P1 rk X p = = and { } 01 PX p == . n We are interested in every time i at which we have just seen the sequence (0,1) or the sequence (1,1), i.e., every time i at which the ordered sequence (0,1) terminates or the sequence (1,1) terminates. Note that the latter sequence can terminate at
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This note was uploaded on 10/21/2010 for the course EE 5581 taught by Professor Moon,j during the Spring '08 term at Minnesota.

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6.262.PS4 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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