Exercise: time until consecutive successes 3 points possible (ungraded) consider a sequence, x, of independent bernoulli random variables with common success probability p 1/4. let t be the first time at which we have a success immediately following a previous success; that is, t = min{n : xn = xn-1 = success). we are interested in ein we model this problem using the following markov chain 3/4 1/4 4 f ss1 1/4 the state s denotes a success, state f denotes a failure, and state ss is an absorbing state denoting the event that we have obtained two successes in a row. calculate the numerical values of the following quantities 1. 2. 3.