We are given that X(t) and Y(t) are uncorrelated jointly wide sense stationary Gaussian random process with autocorrelation functions Rx(T) and Ry(T), whereRxT)=I| Otherwise for It| s 1 and Ry(T) = 6(T).a) Are X(t) and Y(1) independent random process? Why or why not? b) Is X(t) strict sense stationary? Why or why not?c) Find the cross correlation between X(t) and Y(t), that is Rxy(T). d) Find the power spectral density of Y(t), that is Syy (jw).

Q.2. a) What is the difference between the likelihood density function and the a posteriori density function. b) Let x = s + n, where the observed random variable is 'x'. 's' is a random parameter independent of the added random noise 'n'. The probability density of 'n' is given by p(n) = 2 e-2 (n-1) u(n - 1) and the probability density of the parameter 's' is given by p(s) = 1/8 s [u(s) - u(s - 4)]. i) Get Sms. ii) Get Smap. iii) Does 's' have a Smi. Why or why not