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Question 7.EX.3: If the mean-value function of the renewal process {N(t), t ≥......

If the mean-value function of the renewal process {N(t), t ≥ 0} is given by
m(t) = t/2, t ≥ 0, what is P{N(5) = 0}?

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By the one-to-one correspondence of m(t) and F, it follows that {N(t),t ≥ 0} is a Poisson process with rate \frac{1}{2}. Hence,

P\left\{N(5) = 0\right\} = e^{−5/2}

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