f: (1)E[=(t]= ELX, cosOot-X, sin oot] EL X c0S00 ElX2 sin oot ElXcosot-ELX, sm oot=0 E[z(t]= El(X cosoot-X, sin @,)I ELXIcos Wot-2EIXNElX2 cos aotsin @ot+ ElX2sin-Oot o(cos@ot+snoot)-0=0 (2)因为X1X2为正态分布,所以(1)也为正态分布, 又E[z(1)]=0,D[z()=E[=2()-E2[()=a2 所以f(=) O exp 2e (3)R(t12t2)=E[=(t1)2(t2 ELCX, COSOot-x2 sin aot,(X, cosoot2-X2 sin @ot2) ELXi]cos oot, Cos aot2+ ElX2]sin @ot, sin @ot2 ELXIELX2 ]cos@ot, sin oot2-ELX2 ELX,sin @ot, cos@ot2 o cosLOo(t2-tu=O COS Oot B(1,12)=R(12t2)-E[(1)E[=(t2=R(t1,t2)=cosO0                                       0 2 1 2 1 2 1 2 1 2 0 2 0 2 1 2 1 2 0 1 0 2 2 1 0 1 0 2 0 1 0 2 2 0 1 0 2 2 2 1 1 0 1 2 0 1 1 0 2 2 0 2 1 2 1 2 2 2 2 2 2 1 2 2 0 2 0 2 2 0 2 2 0 1 2 0 0 2 2 2 1 2 1 0 2 0 2 1 0 2 0 1 0 2 0 1 0 2 0 ( , ) ( , ) [ ( )] [ ( )] ( , ) cos cos[ ( )] cos [ ] [ ]cos sin [ ] [ ]sin cos [ ]cos cos [ ]sin sin [( cos sin )( cos sin )] 3 ( , ) [ ( ) ( )] ) 2 exp( 2 1 ( ) [ ( )] 0 [ ( )] [ ( )] [ ( )] 2 ( ) (cos sin ) 0 [ ]cos 2 [ ] [ ]cos sin [ ]sin [ ( )] [( cos sin ) ] [ ]cos [ ]sin 0 [ cos ] [ sin ] 1 [ ( )] [ cos sin ] = − = = = − = − − = + = − − = = − = = − = = + − = = − + = − = − = = − = − B t t R t t E z t E z t R t t t t E X E X t t E X E X t t E X t t E X t t E X t X t X t X t R t t E z t z t z f z E z t D z t E z t E z t X X z t t t E X t E X E X t t E X t E z t E X t X t E X t E X t E X t E X t E z t E X t X t （ ） 所以 又 ， （ ）因为 、 为正态分布，所以 也为正态分布， 解：（）