X(t) is a wide sense stationary stochastic process with autocorrelation function RX() = 10sin (21000)/(21000). The process

Question:

X(t) is a wide sense stationary stochastic process with autocorrelation function
RX(τ) = 10sin (2π1000τ)/(2π1000τ).
The process Y(t) is a version of X(t) delayed by 50 microseconds: Y(t) = X(t - t0) where t0 = 5 × 10-5s.
(a) Derive the autocorrelation function of Y(t).
(b) Derive the cross-correlation function of X(t) and Y(t).
(c) Is Y(t) wide-sense stationary?
(d) Are X(t) and Y(t) jointly wide sense stationary?