1. ## poisson

Q.
A customer comes to a gas station at a rate of one every five minutes. what is the probability
(a) that no one comes for 5 mins
(b)that at least 3 cars come during five minutes!??

i know it is poisson but in (a) i dont know what lamda is and why?
and in
(b) i have 1-[e^(-lamda.t)]-[lamda.t.e^(-lambda.t)]-[1/2(lambda.t)^2.e^(-lambda.t)]
that is the answer in the book but I don't see why the "t" is brought down , do you differentiate it or something???

2. Originally Posted by eleahy
Q.
A customer comes to a gas station at a rate of one every five minutes. what is the probability
(a) that no one comes for 5 mins
(b)that at least 3 cars come during five minutes!??

i know it is poisson but in (a) i dont know what lamda is and why?
and in
(b) i have 1-[e^(-lamda.t)]-[lamda.t.e^(-lambda.t)]-[1/2(lambda.t)^2.e^(-lambda.t)]
that is the answer in the book but I don't see why the "t" is brought down , do you differentiate it or something???
He gives you the rate which is 1 (or 1/5 depending on how you look at it). For (a) what is the distribution of the waiting time? For (b) I think you need to look up what the Poisson distribution is.