Question 2.

2. [40 pts]) Consider the random process X(t) = A + B . sin(2n . fo . t + 0), where 0 is a random variable uniformly distributed on 0,2x], A is uniformly distributed on [-3,3], and B is a discrete random variable with equally likely values of [1, 2, 3, 4,5]. All random variables, 0, A. and B, are independent. (a. 6) Find the expected mean value using the pdf's (b. 6) Find the time average mean value. Hint let T = 1/(2 . fo). 1 T (X(t)) = lim - X(t) . dt T-co 2 . T J-T (c. 6) Find the 20 moment using the expected values, E[X(t)~], computation (d. 6) Find the time average of the squared signal (the power). Hint let T = 1/(2 . fo). 1 (X(t)2) = lim T-0 2 . T ( x(t ) ). dt J-T (e. 4) Is this process stationary and ergodic? (e. 12) Find the autocorrelation using the pdf's Rxx(t1, t2) = E[X(t1) . X(t2)]. Can the result be expressed in terms of Rxx(T) , where t = t2 - t1