$($a$)$ Showthatthem.s$.$derivativeofY$($t$)$X$2($t$)$is

Y $($t$)=$ dY$($t$)=2$X$($t$)$X $($t$),$

dt whereX $($t$)=$ dX$($t$)$isthem$.$s$.$derivativeofX$($t$).$

dt

$($b$)$ Determine the ACRF of Y $($t$)$ in terms of RX $($$)$ and its derivatives.

Hint: You will need the following result for jointly Gaussian random variables E$$X$1$ X$2$ X$3$ X$4=$ R$12$R$34+$ R$13$R$24+$ R$14$R$23$

whereRij $=$E$$XiXj$.$