已知随机过程X(t)的自相关函数RX(t1，t2)，试求下列随机过程的自相关函数：

Question

如题所述

Answer 1

【答案】：R_Y(t₁,t₂)=E[Y(t₁)Y(t₂)]=E[X(t₁)(t₁+1)X(t₂)(t₂+1)]=(t₁+1)(t₂+1)E[X(t₁)X(t₂)]=(t₁+1)(t₂+1)R_X(t₁,t₂)$R_Z(t₁, t₂)=E[Z(t₁)Z(t2)]=E[cX(t₁)cX(t₂)]=c²E[X(t₁)X(t₂)]=c²R_X(t₁,t₂)