I'm having trouble doing a classic proof (integration par part and induction on r) for this :
Pr(X>t)=Pr(Y ≤r−1), where X follows a gamma Γ(α = r, β = 1/λ) and Y a Poisson P (λt).
Start with r = 1 (exponential distribution).
I don't really understand what induction on r really means...