Problem 2A frog is in a pond with 5 water lilies numbered from 1 to 5. With exponential rate 1, the frogleaves 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 timet.a. Admitting that X(t) is a continuous-time Markov chain, give its parameters (i.e. the vi and Pijof 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) (nocomputations required).c. Write the forwardd.Chapman-Kolmogorov equation, and prove5-Pu(t).Pir(t) =1=4Solve this equation to compute p₁1(t).that

*Answer: (a) The state space of the Markov chain X(t) is the set of water lilies, which is…

Answered: ts from lily 1. Let X(t) be the number…

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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Q6 You have two machines. Machine 1 has a lifetime T which is exponentially distributed with parameter d1, and Machine 2 has a lifetime T, which is exponentially distributed with parameter A, and is independent of T1. Machine 1 starts at time 0, and Machine 2 starts at a time T > 0. Q6(i.) Assume that T is deterministic. Compute the probability that Machine 1 is the first to fail. Q6(ii.) Answer the same question when T is exponentially distributed with parameter u and is independent of T1 and T,.
(Section 1.7) Consider the DTDS reperesented by the following table: Enter the updating function for this DTDS: ht+1 ht+ = Enter the solution function for this DTDS: h(t) = t ht ht+1 3 0 1 2 WN 3 615 w 7 9 561U 7 9 11

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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).