Communication Signal (CS)
Question 1: Random Variable
August 2016 Problem 4
Solution
Since $ X(t) $ is a wide sense Gaussian Process $ \Rightarrow X(t) $ is SSS.
$ Y(t) $ is a combination of two Gaussian distribution.
$ R_{x(t)x(t+\tau)}=R_{xx}(\tau) $
Such that
$ Y(t)=c_1X(t)-c_2X(t-\tau) $ $ \sim N((c_1-c_2)\mu_x),(c_1^2+c_2^2)\sigma_x^2-2c_1c_2R_{xx}(\tau)) $
