RP-Midterm Exam - Kyung Hee University Department of...

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1 Kyung Hee University Department of Electronics and Radio Engineering C1002900 Random Processing Midterm Exam Spring 2010 Professor Hyundong Shin April 26, 2010 19:00 – 21:30 (150 minutes) This is an in-class closed book exam, but one A4-size sheet of notes (single side) is allowed. A correct answer does not guarantee full credit, and a wrong answer does not guarantee loss of credit. You should clearly but concisely expose your reasoning and show all rele- vant work . Your grade on each problem will be based on our best assessment of your level of understanding as reflected by what you have written in the answer sheets. Please be neat we cannot grade what we cannot decipher! Problem 1 (10 points) Arrivals of certain events at points in time are known to constitute a Poisson random variable, but it is unknown which of two possible values of the average arrival rate describes the ran- dom variable. Our a priori estimate is that  2 or 4 with equal probability. We observe the random variable for t units of time and observe exactly k arrivals. Given this information, de- termine the conditional probability that 2 . Check to see whether or not your answer is rea- sonable for some simple limiting values for k and t . Problem 2 (15 points) (a) (5 points) Let   , X 01 and   , Y be statistical independent. Consider a complex random variable Z Xj Y  . Find the probability that the instantaneous power
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RP-Midterm Exam - Kyung Hee University Department of...

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