16. Consider a renewal process N(t) with associated distribution function F(x). Define m(t) = E[N(t)]. Show that m(t) satisfies the renewal equation ma(1) = z₂(1) + √m(t—t) dF(t), where (1) JE()‚‹- Hint: Use the renewal argument. k= 1, 2, ..., m(t-t) dF(t).

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Author:Amos Gilat
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16. Consider a renewal process N(t) with associated distribution function F(x).
Define m,(t) = E[N(t)*]. Show that m,(t) satisfies the renewal equation
m,() =#¾(e) + J m,(t – t) d F(t),
k= 1, 2, ...,
where
m(t -
dF(t).
Ilint: Use the renewal argument.
Transcribed Image Text:16. Consider a renewal process N(t) with associated distribution function F(x). Define m,(t) = E[N(t)*]. Show that m,(t) satisfies the renewal equation m,() =#¾(e) + J m,(t – t) d F(t), k= 1, 2, ..., where m(t - dF(t). Ilint: Use the renewal argument.
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