设随机过程X(t)=Ucos2t 其中U为随机变量 且E(U)=5 D(U)=6 试求:
变量,过程
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设随机过程X(t)=Ucos2t,其中U为随机变量,且E(U)=5,D(U)=6,试求:
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mX(t)=E(Ucos2t)=cos2tE(U)=5cos2t$RX(t1,t2)=E[X(t1)X(t2)]=E(Ucos2t1Ucos2t2)=cos2t1cos2t2E(U2)=cos2t1cos2t2(6+52)=31cos2t1cos2t2
CX(t1,t2)=RX(t1,t2)-mX(t1)mX(t2)=31cos2t1cos2t2-25cos2t1cos2t2=6cos2t1cos2t2$DX(t)=CX(t,t)=6cos2tcos2t=6cos22t
