Question: Let m(t) = E[N(t)] be the renewal function for a renewal process. m(t) =Fx(t) + ? m(t ? x)fx(x) dx (b) Use this expression to

Let m(t) = E[N(t)] be the renewal function for a renewal process. m(t) =Fx(t) + ? m(t ? x)fx(x) dx

(b) Use this expression to show that Jo fx (t - y)m'(y) dy = m'(t) - fx(t). (c) Assume that g (t) is a probability function or expectation satisfying the renewal equation g(t) = h(t) + Jog(t - x)fx(x) dx. Convolve both sides with m'(t) to show that g (t) = h(t) + S h(t - x)m'(x) dx

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