Full Question: The average rate of job submissions in a computer center is 2 per minute. If it can be assumed that the number of submissions per minute has a Poisson distribution, calculate the probability that
(a) more than two jobs will arrive in a minute
$P(X>2) = 1- P(X≤ 2) = 1- [P(X=0)+P(X=1)+P(X=2)]$
and I got 0.3233235 as my answer. Is that correct?
Example: For $P(X=1),$ I did $((2^1)(e^-2))/1!$
(b) at least 30 sec will elapse between any two jobs
This is where I'm confused. A similar problem was answered using Exponential distribution in the book even though the question said this was a Poisson distribution problem.
I tried with Exponential and this is what I got:
Since 30 seconds is $1/2$ of 1 minute, $(1/2) * λ$ or $(1/2)*2 = 1$
$P(X ≥ 1/2) = 1 - P(x < 1/2) = 1 - (1- e^-1) = 0.3678794$
Please tell me if I used the correct distribution functions for both a and b, and if I answered them correctly. Thank you.