45. Let {N(t), t 0} be a Poisson process with rate , that is independent of the...

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45. Let {N(t), t 0} be a Poisson process with rate λ, that is independent of the nonnegative random variable T with mean μ and variance σ2.

Find

(a) Cov(T, N(T )),

(b) Var(N(T )).

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