At time there are an infinite t = 0 number of molecules of type a and 2n molecules of type b in a two-component gas mixture. After an exponential random time with parameter µ any molecule of type b combines, independently of the others, with a molecule of type a to form a molecule ab.
(1) What is the probability that at time t there are still j free molecules of type b in the container?
(2) What is the mean time till there are left only n free molecules of type b in the container?