# Question

Suppose the power line in the previous problem has an impulse response that may be approximated by h (t) = te– atu (t), where a = 10s– 1.

(a) What does the shot noise on the power line look like? Sketch a possible member function of the shot noise process.

(b) Find the mean function of the shot noise process.

(c) Find the autocorrelation function of the shot noise process.

(a) What does the shot noise on the power line look like? Sketch a possible member function of the shot noise process.

(b) Find the mean function of the shot noise process.

(c) Find the autocorrelation function of the shot noise process.

## Answer to relevant Questions

A shot noise process with random amplitudes is defined by Where the Si are a sequence of points from a Poisson process and the Ai are IID random variables which are also independent of the Poisson points. (a) Find the mean ...Let X (t) be a Weiner process with diffusion parameter λ as described in Section 8.5. Determine whether or not X (t) is mean square continuous. Find the PSD of the process described in Exercise 8.1. For a Markov chain, prove or disprove the following statement: Pr (Xk = ik | Xk + 1 = ik + 1, Xk + 2 = ik + 2… Xk+ m = ik+ m) = Pr (Xk = ik | Xk + 1 = ik + 1) A certain three- state Markov chain has a transition probability matrix given by Determine if the Markov chain has a unique steady- state distribution or not. If it does, find that distribution. For a Markov chain with each of the transition probability matrices in (a)–( c), find the communicating classes and the periodicity of the various states. (a) (b) (c)Post your question

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