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7) (20 pts) Let X(t) = At be a random process, such that A is N(0,...

7) (20 pts) Let X(t) = At be a random process, such that A is N(0, 1). , ??(t)-EX(t)]. (a) Find mean of the random process X(t) (b) Find the auto-correlation function of X, Rx(t1,t2) - E[X (ti)X (t2)

7) (20 pts) Let X(t) = At be a random process, such that A is N(0, 1). , ??(t)-EX(t)]. (a) Find mean of the random process X(t) (b) Find the auto-correlation function of X, Rx(t1,t2) - E[X (ti)X (t2)
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As \space\ A\sim\mathcal{N}(0,1), E[A]=0.\\ \therefore E[X(t)]=E[At]=0\\i.e.\space\ \mu _{X}(t)=0 \\\\R_{X}(t_{1},t_{2})=E[X(t_{1})X(t_{2})]=E[At_{1}\cdot At_{2}]=E[A^{2}t_{1}t_{2}] =t_{1}t_{2}E[A^{2}]\\=t_{1}t_{2}\cdot var(A)\\=t_{1}t_{2}

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7) (20 pts) Let X(t) = At be a random process, such that A is N(0,...
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