I don't know how to solve this. do provide step by step solution ans explanation if possible

Question 1 (20 pts). Let XE Zzo be the amount of water (say measures in the unit of hundred million gallons) in MacRitchie Reservoir at noon on day n. During the 24 hours period beginning at this time. Yn E Zxo units of water flows into the reservoir. The maximum capacity of the reservoir is 5 units, and excessive inflows are spilled and lost. Just before noon on each day, exactly 1 unit of water is removed if the reservoir is non-empty, and no water is removed if the reservoir is dried up. Assume that Y1.Y2.... are iid discrete RVs, where? 1 Pr(Y1 = 0) Pr(Y1 = 1) = 0= 1 Pr(Y2 = 2) = 7 1 1 Pr(Y1 = 3) - Pr(Y1 = 4) 12 3 Show that {Xn}= forms a DTMC, and write down the transition probability matrix. distributed as Uniffin. 1}). that is. Question 1 (20 pts). Let XE Zzo be the amount of water (say measures in the unit of hundred million gallons) in MacRitchie Reservoir at noon on day n. During the 24 hours period beginning at this time. Yn E Zxo units of water flows into the reservoir. The maximum capacity of the reservoir is 5 units, and excessive inflows are spilled and lost. Just before noon on each day, exactly 1 unit of water is removed if the reservoir is non-empty, and no water is removed if the reservoir is dried up. Assume that Y1.Y2.... are iid discrete RVs, where? 1 Pr(Y1 = 0) Pr(Y1 = 1) = 0= 1 Pr(Y2 = 2) = 7 1 1 Pr(Y1 = 3) - Pr(Y1 = 4) 12 3 Show that {Xn}= forms a DTMC, and write down the transition probability matrix. distributed as Uniffin. 1}). that is