Let a homogeneous Poisson process have intensity \(\lambda\), and let \(T_{i}\) be the time point at which the \(i\) th Poisson event occurs. For \(t \rightarrow \infty\), determine and sketch the covariance function \(C(\tau)\) of the shot noise process \(\{X(t), t \geq 0\}\) given by

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N(t) X(t) = h(t-T;) with h(t)= sin for 0IST 0, elsewhere