An ecologist wants to examine the deer population in two different areas, Area 1 and Area 2. He assumes that the number of deer, X and Y, in Areas 1 and 2 is Poisson distributed.

The ecologist reckons that the expected number of deer is 1 = 3 in area 1 and 2 = 5 in area 2 respectively. Find P (X = 2) and P (X 3), and find an approximate expression for P (X = Y). Clarify the assumption you use to calculate the last answer.

If a deer is in such an area, the ecologist assumes a probability of 0.2 that it is observed. If in reality there are 5 deer in the area, what is the probability that three of them are observed? What is the expected number of deer observed?

if you can help me and go in to detail, it would help alot :)