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Unformatted text preview: ECE 302, Homework #13. Due date: 4/27 http://www.ece.purdue.edu/ chihw/ECE302 07.html Prof. Chih-Chun Wang Email: email@example.com Office: MSEE354 Office Hours: MWF: 12pm1pm TA: Kamesh Krishnamurthy, Email: firstname.lastname@example.org Office: POTR 370 Office Hours: M: 1011am TTh: 10:30am12:30pm Question 1: Consider a random process X ( t ) = W + (2 Y- 1) t , where Y is a Bernoulli random variable with parameter p = 1 / 3 and W is the outcome of a 6-faced fair dice. We further assume Y and W are independent. 1. Find the probability that P ( X (1 . 5) > 3). 2. Find the probability that P ( X (1 . 5) < X (2 . 5)). 3. Find the probability that P ( X ( t ) > 3 for all t in (1 , 2)). Hint: There are at most 12 possible candidates of X ( t ). Question 2: Continue from the previous question. 1. Find the mean function M X ( t ). 2. Find the auto-correlation function R X ( t 1 ,t 2 ). 3. Find the auto-covariance function C X ( t 1 ,t 2 )....
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- Spring '08