Problem 3.2 (10 points) Consider a two-state continuous time Markov chain with state space {1,2} and transition function Ac (t) = MC (A4)t Ac (A+0) = hle (A4) P(t) = 4 | / (t > 0) Find P[Xo ≤ 2 | Xo = 1]: Find P[X1 = 1, X2 = 2 | X1 = 1]
Added by Paul A.
Close
Step 1
From the given transition function, we can write: P(1,1) = Ac(1)Ac(1) = 1/4 P(1,2) = Ac(1)Ac(2) = 3/4 P(2,1) = Ac(2)Ac(1) = 1/2 P(2,2) = Ac(2)Ac(2) = 1/2 where Ac(1) and Ac(2) are the arrival rates for states 1 and 2, respectively. We don't have this Show more…
Show all steps
Your feedback will help us improve your experience
Jainendra Ojha and 95 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let X be a continuous-time Markov process with two states {1,2} and P be the transition matrix with entries p_ij(t). Prove that P(X(t) = 2 | X(0) = 1, X(3t) = 1, X(4t) = 1) is equal to (p_12(t)p_21(2t)) / p_11(3t).
Ameer S.
Problem 2 The Markov chain X = {Xn}n=0 to infinity has state space X = {a, b, c} and P = [[0, 0.5, 0.5], [0.5, 0, 0.5], [0.5, 0.5, 0]] 2.1 [10 points] Is this Markov chain ergodic? 2.2 [10 points] Find the long run proportion of time the chain spends in the state c.
Adi S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD