Consider a renewal process {N(t), t 0} having a gamma (r, ) interarrival distribution. That is,

Consider a renewal process {N(t), t ≥ 0} having a gamma (r, λ) interarrival distribution. That is, the interarrival density is

where [i/r] is the largest integer less than or equal to i/r.
Hint: Use the relationship between the gamma (r, λ) distribution and the sum of r independent exponentials with rate λ to define N(t) in terms of a Poisson process with rate λ.

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f(x)= dex (x)-1 (r - 1)! (a) Show that P{N(t)n} = x>0 e-t (21) i! i=nr (b) Show that m(t)= e-t (t)i i! i=r