MATH 632 Midterm: 2004 Math 632 - Spring Exam 1
Document Summary
Instructions: show calculations and give concise justi cations for full credit. Don"t forget that theoretical ideas can help avoid tricky computations. Imagine a road traveled by two kinds of vehicles, trucks and cars. Find the invariant distribution of the markov chain. (b) (15 pts) find the limit lim n . In words, this is the long-term probability that two consecutive vehicles con- tain at least one truck. For the sake of de niteness, we are assuming that the rst vehicle we see is a car. (c) (15 pts) for each integer k, let k be the random index such that x k is the kth truck. In words, this is the probability that the kth truck is followed by two cars: fix constants , (0, 1) such that + < 1, and consider the. Markov chain on the state space s = {1, 2, 3, 4} with transition matrix.
