I need to find the limiting distribution for this however to do that I need to first find its transition diagram and I'm just stuck on thinking about how this M.C works.
I'm not even sure on the state space for this chain $$X_n=(L_n,R_n)$$Any help with the transition diagram is appreciated =)
Kind of late reply as I havn't been on but that's what I ended up doing so your answer agrees with me -> The M.C consists of 4 states (0,0) , (1,0) , (0,1) , (1,1) and then you find the transition probabilities for each state using what you've given.