4. The number of bacteria colonies of a certain type in sample of polluted water has a Poisson distribution with a mean of 2 per 1-cubic centimeter. (a) Find the probability that a 1-cubic centimeter sample taken from this water will have no bacteria colonies. (b) Find the probability that a 1-cubic centimeter sample taken from this water will have at least two bacteria colonies. (c) Find the expected number and variance of the number of bacteria colonies in a 1-cubic centimeter sample taken from this water. (d) If 10 independent 1-cubic centimeter samples are taken from this water, find the proba- bility that exactly 3 of these samples will contain two or more bacteria colonies