Acomponent of a computer has an active life, measured in discrete units, that is a random variable t where p(t = 1) = 0.4, pt = 2) = 0.6. suppose one starts with a fresh component and each component is replaced by a new component upon failure. define a markov chain xn, n = 0,1, by letting xn be the age of the component in service at time n. the lifetimes of consecutive components are independently distributed. we also take the convention that xn = 0 at the time of failure. the state space of xn is {0, 1}. as an example, if the first component works for 2 periods and the second component works for 1 periods, then we have x% = 0, x1 = 1, x2 = 0, x3 = 0, (1). determine the long run probability that a failure occurs in a single period. hint: this is related to the limiting distribution of xn. (2). what is the expected time between failures?