1. ## Poisson Distribution

Suppose that the number of inquiries arriving at a certain interactive system follows a Poisson distribution with arrival rate of 12 inquiries per minute. Find the probability of 10 inquiries arriving

(a) in a 1-minute interval
(b) in a 3-minute interval

I am unsure if the rate is 60/12 or 12/60.

2. just keep it in minutes

$\lambda=12$ in part a and $\lambda=36$ in part b

$P(X=x)={e^{-\lambda}\lambda^x\over x!}$

(a) $P(X=10)={e^{-12}{12}^{10}\over (10)!}$

(b) $P(X=10)={e^{-36}{36}^{10}\over (10)!}$