At a rival company, IntelligentData, a recruitment drive means that new employees join IntelligentData according to a Poisson process with rate 10 per month. You should assume that the recruitment drive lasts indefinitely. These new recruits leave IntelligentData as an emigration process with rate 1 per month. 

Let {Yt: t ≥ 0} denote the number of employees who joined IntelligentData during the recruitment drive and are still working there at time t. 

Does the number of employees at IntelligentData converge to an equilibrium distribution? Justify your answer. If you think it does converge, write down the equilibrium distribution. If you think that it doesn't, explain how you could change the immigration and emigration rate so that it does (there is no need to give the equilibrium in this case but you should give an example of a set of immigration and emigration rates that would guarantee an equilibrium where neither the immigration or emigration rate is zero).

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Let us assume that the time taken for the ith new employee to appear in Intellige... View the full answer