5531F2009hmk2

5531F2009hmk2 - EE 5531 F2009 Homework Set 2 due by 4:30pm...

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EE 5531 F2009 Homework Set 2 — due by 4:30pm Wed Sept. 23 Problem 1 Let ( T i : i =1 , 2 , 3 , ··· ) be an IID process in which each T i is exponentially distributed with mean 1 / 2. Let ( S i : i , 2 , 3 , ) be an IID process in which each S i is exponentially distributed with mean 1 / 3. (Assume that the T process and the S process are independent as well.) Let ( W i : i , 2 , ) be the random process in which W i = ( 0 ,i max(0 ,W i 1 + S i 1 T i 1 ) ,i> 1 It is known that there is a strong law of large numbers for the W process. That is, there is a real constant C such that W 1 + W 2 + + W i i a.s. C. Use Matlab to estimate the value of C ; you might need to look in the EE 3025 Matlab instructional materials to see how to simulate the value of an exponentially distributed RV. C will turn out to be a pretty simple rational real number between 0 and 1; what do you think the value of C might be based on your Matlab experiments? (Use 50000 W time samples in your Matlab runs, which will give you enough accuracy to make the proper conclusion.) (Note: We will discuss in class the meaning of the T, S, and W processes.)

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5531F2009hmk2 - EE 5531 F2009 Homework Set 2 due by 4:30pm...

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