Given a Poisson process with an average, a arrivals per unitof time, find the probability that there will be no arrivals during a time interval of length, t,
namely, the probability that the waiting times
between successive arrivals will be at least of
length t.

Question

Given a Poisson process with an average, a arrivals per unitof time, find the probability that there will be no arrivals during a time interval of length, t, 
namely, the probability that the waiting times
between successive arrivals will be at least of 
length t.

anonymous · Answer

I think I have to use the gamma distribution formula here

anonymous · Answer

$$f(x)=\frac{ 1 }{ \beta^{\alpha}\Gamma(\alpha) }x^{\alpha-1}e^{-x/\beta}$$
for x>0, alpha>0,Beta>0