If one extends the definition of renewal processes to include inter-renewal intervals of duration 0, with Pr{X=0} = α, show that the expected number of simultaneous renewals at a renewal epoch is 1/(1...

If one extends the definition of renewal processes to include inter-renewal intervals of duration 0, with Pr{X=0} = α, show that the expected number of simultaneous renewals at a renewal epoch is 1/(1 - α), and that, for a non-arithmetic process, the probability of 1 or more renewals in the interval (t,t + δ] tends to (1 - α)/E[X] + o(δ) as t → ∞.