Question: (c) Suppose that 3 = (3(t ) : t 0) is a non-negative, real-valued random process. Conditional on 3, let N = (N(t) :

(c) Suppose that 3 = (3(t ) : t ≥ 0) is a non-negative, real-valued random process. Conditional on 3, let N = (N(t) : t ≥ 0) be an inhomogeneous Poisson process with rate function 3(u). Such a process N is called a doubly stochastic Poisson process. Show that the variance of N(t ) cannot be less than its mean.

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