Steve and his friends are relaxing at a local tavern. The number of drinks that Steve's table receives is Poisson distributed with an average of 9 drinks per 3 hours. Write out the distribution and parameters you are using in each part below.
a) Find the probability that Steve's table receives between 2 and 4 drinks inclusive in the first hour.
b) What is the probability that it takes until the 4th hour before there is an hour in which Steve's table receives between 2 and 4 drinks inclusive?
c) Knowing that Steve's table received 10 drinks in the first 2 hours, what is the probability that at least 2 of the drinks came with in the first 30 minutes?
d) Assume Steve's table just received a drink. Find the probability that the next drink is received at least 15 minutes from now.