Transcribed Image Text from this QuestionProblem # 1.0 A continuous-time stochastic process X(t) with t € (-1, 1) is def

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Transcribed Image Text From This Questionproblem 1 0 A Continuous Time Stochastic Process X T With T 1 1 Is Def 1 (141.82 KiB) Viewed 100 times

Transcribed Image Text from this QuestionProblem # 1.0 A continuous-time stochastic process X(t) with t € (-1, 1) is defined via: X(t) =T – (1 – t), w E12, where T ~ U([0,1]). For this process: 1.a) plot two sample realizations xi(t) and x2(t). 1.b) Determine the first-order CDF and PDF Fx(x; t) and fx(x; t) associated with this process. 1.c) Determine the mean Mä(t) and the variance oz(t) associated with this process. Is this process first-order stationary? Justify your answer. 1.d) Determine the auto-correlation Rxx(t1, tz) and the auto-covariance Cxx(t1, t2) associated with this process. Is this process second-order stationary? Jus- tify your answer properly.