Consider a miner trapped in a room that contains three doors. Door 1 leads him to freedom after two days of travel; door 2 returns him to his room after a four-day journey; and door 3 returns him to his room after a six-day journey. Suppose at all times he is equally likely to choose any of the three doors, and let T denote the time it takes the miner to become free. (a) Define a sequence of independent and identically distributed random variables X_1, X_2, and a stopping time N such that T=Sigma_i=1^N X_i (b) Use Wald's equation to find E[T]. (c) Compute E[Sigma_i=1^N=X_i|N=n]and note that it is not equal to E[Sigma_i=1^N=X_i]. (d) Use part (c) for a second derivation of E[T]