The problem:

The number of ships X that arrive to a certain harbor in one day is Poisson

distributed with E(X) = 2. The harbor can handle no more than 3 ships per day. The rst

3 ships to arrive each day are served. Other ships are redirected to other harbours

a) What number of ships to arrive on single day has the highest probability? What is the

probability that on a given day, one or more ships will have to be redirected?

b) What is the expected number of ships to be served on a given day?

c) How big must the harbour be to make the probability that all ships that arrive will be

served, at least 90%?

I found a to be pretty straight forward, and got the right answer. However, I am struggling on b and c.