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ts from lily 1. Let X(t) be the number of the lily is a continuous-time Markov chain, give its para f is required. (t) = j|X(0) = 1). Explain why P12(t) = equation to compute p₁1(t). P13(t Chapman-Kolmogorov equation, and prove that 5 P₁₁(t) = 1- P₁i(t). 7²11(t).

ts from lily 1. Let X(t) be the number of the lily is a continuous-time Markov chain, give its para f is required. (t) = j|X(0) = 1). Explain why P12(t) = equation to compute p₁1(t). P13(t Chapman-Kolmogorov equation, and prove that 5 P₁₁(t) = 1- P₁i(t). 7²11(t).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problem 2 A frog is in a pond with 5 water lilies numbered from 1 to 5. With exponential rate 1, the frog leaves its current water lily, chooses a new one uniformly among the four others and jumps to it. We assume the frog starts from lily 1. Let X(t) be the number of the lily where the frog is at time t. a. Admitting that X(t) is a continuous-time Markov chain, give its parameters (i.e. the vi and Pij of the course). No proof is required. b. Let pij(t) = P (X(t) = j|X(0) = 1). Explain why p12(t) P13(t) = P14(t) = P15(t) (no computations required). c. Write the forward d. Chapman-Kolmogorov equation, and prove 5 -Pu(t). Pir(t) = 1 = 4 Solve this equation to compute p₁1(t). that
Transcribed Image Text:Problem 2 A frog is in a pond with 5 water lilies numbered from 1 to 5. With exponential rate 1, the frog leaves its current water lily, chooses a new one uniformly among the four others and jumps to it. We assume the frog starts from lily 1. Let X(t) be the number of the lily where the frog is at time t. a. Admitting that X(t) is a continuous-time Markov chain, give its parameters (i.e. the vi and Pij of the course). No proof is required. b. Let pij(t) = P (X(t) = j|X(0) = 1). Explain why p12(t) P13(t) = P14(t) = P15(t) (no computations required). c. Write the forward d. Chapman-Kolmogorov equation, and prove 5 -Pu(t). Pir(t) = 1 = 4 Solve this equation to compute p₁1(t). that
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