guys! I need help for this

Discrete Time Markov Chains/ First Passage Times l. A bus with passenger capacity K stops at stations numbered 0,1,2,3 on an unlimited route. Denote by Xn the number of passengers waiting to board the bus at station n. Assume that {Xwn 2 0} are iid random variables with common distribution ak = P(Xn = k),k = 0,1,2, Each passenger on the bus leaves at any given station with constant probability p, independently from the other passengers. Once people have exited, as many passengers waiting at a given station will board as there are free places on the bus available. Denote by Znthe number of passengers on the bus after leaving station n. Show that {Zm n 2 0} is a DTMC and calculate its transition probability matrix. 2. Consider the DTMC in problem 4 with the capacity K = 20, Xn ~ Poisson(10), and p = 0.4. Calculate E(Xn|X0 = 0) forn = 0,1,2, ...20