JerJason 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. one year ago one year ago

1. JerJason

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

2. JerJason

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

3. UnkleRhaukus

wouldn't it be a Poisson distribution?