I remember something about the exponential distribution being the time between Poisson processes, but not sure how to apply it here.Sightings of a particular species of rare bird occur at a rate of 6 per year. Assume that sightings can be modelled by a Poisson process \(\displaystyle (N(t), t>0)\) where time \(\displaystyle t\) is measured in years and time 0 is the present time.

Let \(\displaystyle T_1\) be the time from time 0 until the 1st sighting. What is the probability that \(\displaystyle T_1\) is at most:

i) 1.

ii) 2.

Would \(\displaystyle T_1\) be distributed \(\displaystyle Ex(12)\)?

Thanks in advance