The number of bacteria colonies of a certain type in sample of polluted water has a Poissondistribution with a mean of 2 per 1-cubic centimeter.(

a) Find the probability that a 1-cubic centimeter sample taken from this water will haveno bacteria colonies.

(b) Find the probability that a 1-cubic centimeter sample taken from this water will haveat least two bacteria colonies.

(c) Find the expected number and variance of the number of bacteria colonies in a 1-cubiccentimeter 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.