Outworld Devourer's Mana Pool. There is a hero called Outworld Devourer in your

favorite game. Initially, his mana pool is at 100%. Every hit he makes on his enemy is very powerful but

drains 1 of his mana pool. However, after every hit, with probability p, he will automatically restore the n

mana he lost with the hit. He will keep hitting until there's no mana left in his mana pool.

1. a)Use a Markov chain to represent Outworld Devourer's mana pool, define the states and write down the transition probabilities, either in a graph or as a matrix. Which state(s) are recurrent and which
2. state(s) are transient?
3. b)Denote the number of total hits on his enemy as a random variable, X. Find the PMF of X.
4. c)Find the expected value of X.