The Colorall Paint factory uses "agent A" in the paint manufacturing process. There is an average of 3.45 particles of agent A in a cubic metre of the air emitted during the production process. (a) Let X = the number of particles of agent A in a cubic metre of the air emitted. What is the probability distribution of X? (b) What is the probability that there will be five particles of agent A in a cubic metre of air emitted from the factory? (c) What is the probability that there will be at least four particles of agent A in a cubic metre of air emitted from the factory? (d) Find the expected value, variance and the standard deviation of X.