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In this problem we develop an alternative derivation for the

In this problem, we develop an alternative derivation for the mean function of the shot noise process described in Section 8.7,

Where the Si are the arrival times of a Poisson process with arrival rate, λ, and h (t) is an arbitrary pulse shape which we take to be causal. That is, h (t) = 0 for t < 0. In order to find the mean function, µX (t) = E [X (t)], we condition on the event that there were exactly n arrivals in [0, t]. Then, the conditional mean function is

Derive the auto covariance function of the shot noise process.

Where the Si are the arrival times of a Poisson process with arrival rate, λ, and h (t) is an arbitrary pulse shape which we take to be causal. That is, h (t) = 0 for t < 0. In order to find the mean function, µX (t) = E [X (t)], we condition on the event that there were exactly n arrivals in [0, t]. Then, the conditional mean function is

Derive the auto covariance function of the shot noise process.

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