please solve and give correct answer

1. A reservoir is used to feed a hydroelectric plant located downstream at a rate of 1 unit per period. The reservoir has a maximum storage capacity of 5 units and receives inflows according to the i.i.d. random variables {Y, : n > 1} with distribution P(Y, = 1) = 1, P(Y, = 0) = 3. a. Let Xn E {0, 1, . .., 5} be the amount of water in the reservoir. Show that {X, : n > 0} i a Markov chain. b. Let T = min{n > 0 : X2 =0} denote the time to depletion. Compute E[T| Xo = k] when k E {1, 2, 3, 4 }