There is a question in a textbook which states the following:
Arrivals are modelled as being from a Poisson process with rate r per minute. Given that 2 arrivals occur in a particular minute, at what time do you expect the first and second arrivals?
Hint: Does your answer depend on r?
My thoughts are that, as the arrivals are independent and identically distributed (as assumed from the Poison process from the textbook) and we have 2 in a single minute. We expect the first to occur after 30 seconds and the second after a minute. Is this correct? And why exactly - are the arrivals uniformly distributed over the minute? Or could we say we have a new Poisson process with rate 2 per minute instead of r?
Thank you in advance!