# RP-HW6 - Kyung Hee University Department of Electronics and...

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1 Kyung Hee University Department of Electronics and Radio Engineering C1002900 Random Processing Homework 6 Spring 2010 Professor Hyundong Shin Issued: June 8, 2010 Due: June 16, 2010 (No acceptance of overdue submission) Reading: Course textbook Chapters 9.1-9.3, 10.1-10.2, 11.4, 12.1, 16.2, and Lecture Notes XI-XVI HW 6.1 A random process   Xt is defined as  , , Yt Zt   where , YZ and are statistically independent unit-variance Gaussian random variables with means  . EY EZ E   1 1 0 Clearly justify your answer of each question. (a) Is   a Gaussian random process? (b) Is   strict-sense stationary (SSS)? (c) Is   a Markov process? (d) Is   an independent increment process? HW 6.2 (a) Let   be a random telegraph process. Specifically, let   Nt be a Poisson counting process with   . ! k t te Nt k k   Let   X  01 with probability 1/2 and define     Xt X .

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2 Find   X t ,   , XX K ts ,    Xt f x , and   Xt Xs f xy . (b) Let   be a Gaussian random process with   ,. X XX t Kt se   2 0 Let   f x and   f . Show that   is not an independent increment process. (c) Let     cos Y t  22 where Y and   ,  02 are statistically independent random variables with Y fy y  2 4 44 .
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• Spring '10
• HyungdongShin
• Probability theory, Stochastic process, Kyung Hee University Department of Electronics, independent increment process

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RP-HW6 - Kyung Hee University Department of Electronics and...

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