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7. Suppose (X(t), t≥ 0) is a continuous-time Markov chain with state space S = {1,2,3,4} and transition rates q(i, j) = 1/2 for all i, jES with i j. Suppose that X(0) = 2. Let J₁ min{t: X(t) #2}. = (a) Calculate P(J₁ ≤ 2). (b) Calculate P(X(J₁) = 3).

7. Suppose (X(t), t≥ 0) is a continuous-time Markov chain with state space S = {1,2,3,4} and transition rates q(i, j) = 1/2 for all i, jES with i j. Suppose that X(0) = 2. Let J₁ min{t: X(t) #2}. = (a) Calculate P(J₁ ≤ 2). (b) Calculate P(X(J₁) = 3).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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7. Suppose (X(t),t > 0) is a continuous-time Markov chain with state space S = {1,2,3, 4} and transition rates q(i, j) = 1/2 for all i, j e S with i ± j. Suppose that X (0) = 2. Let J = min{t : X(t) # 2}. (a) Calculate P(Ji < 2). (b) Calculate P(X(J1) = 3).
Transcribed Image Text:7. Suppose (X(t),t > 0) is a continuous-time Markov chain with state space S = {1,2,3, 4} and transition rates q(i, j) = 1/2 for all i, j e S with i ± j. Suppose that X (0) = 2. Let J = min{t : X(t) # 2}. (a) Calculate P(Ji < 2). (b) Calculate P(X(J1) = 3).
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