Calls are received at a company call center according to a Poisson process at the rate of five calls per minute.
(a) Find the probability that no call occurs over a 30-second period.
(b) Find the probability that exactly four calls occur in the 1st minute, and six calls occur in the second minute.
(c) Find the probability that 25 calls are received in the 1st 5 minutes and six of those calls occur in the 1st minute.
(b) $P(N_1=4, N_2=6) \\= P(N_1=4)\cdot P(N_2=6) \\= ...$
As far as I understand, the problem talks about two different time spans. So, $(N_1=4)$ and $(N_2=6)$ should be independent.
Another notion could be:
$P(N_1=4, N_2=6) \\= P(N_1=4, N_2 - N_1 = 6) \\= P(N_1=4, N_1=6) \\=P(N_1=4) \cdot P(N_1=6)$
Which one is correct and why?