Watto's junk shop in Mos Espa can keep at most 2 podracing engines in inventory at a time. The number of podracing pilots (N) coming into his shop on a daily basis follows the pmf P(N = n) = 0.5, n = 0
0.4, n = 1
0.1, n = 2
At the beginning of the day, if Watto has less than a full inventory, he will contract some Jawas to scavenge the desert for a podracing engine he can repair and sell. On any given day, the Jawas are successful at locating an engine 35% of the time. If the Jawas were successful, they will bring Watto the engine that night after he closes his shop. They can only bring him at most one engine per day. Create a DTMC to model his daily inventory levels.
A) What is the state space of the DTMC?
B) Give an equation for tomorrow's starting inventory level as a function of today's inventory level, random demand and resupply amounts.
C) List all possible random outcomes and their resulting probability of occurring.
D) Give the TPM.
E) Draw the TPD.
F) What is the probability Watto has a full inventory two days after having no engines in inventory?