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

Question

anonymous · Answer

The answer my book gets is $$e^{-\alpha t}$$ but I'm unsure of what formula to use to obtain that answer.

anonymous · Answer

I'm thinking maybe gamma distribution:
$$f(x)= \frac{ 1 }{ \beta^{\alpha}\Gamma(\alpha) }x^{\alpha -1}e^{-x/\beta}$$
for x>0, alpha>0, beta>0

unklerhaukus · Answer

wouldn't it be a Poisson distribution?