Please find the questions in the image.

1. Show that if y(t)=x(t+a) - x(t-a), then (a) Ryy( t) = 2 Rxx( 7) - Rxx( T+2a) - Rxx( T-2a) (b) Syy(@) = 4 5xx(@) sinaw 2. Show that if R( z) is the inverse Fourier transform of S(@)20, then Ea,a' R(T, - 7) 20 3. Find Ely(t)}, Ely' (t)}, and Ry( ) if y "(t) + 4y'(t)+13y(t) =26+v(t) and v(t) is white Gaussian noise with variance of 1. 4. The process x(t)=e" is a family of exponentials depending on the random variable a. Find the mean n(t), the autocorrelation function R(t1,t2), and the first-order density f(x,t) of x(t) in terms of the density fala) of a. 5. The process x(t) is real with autocorrelation Rxx(t), show that Pix(t+z) - x(T)|za; s2[R(0) -R(T)]/ a