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
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
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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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 p1j (t) = P (X(t) = j|X(0) = 1). Explain why p12(t) = p13(t) = p14(t) = p15(t) (no
computations required).
c. Write the forwards Chapman–Kolmogorov equation, and prove that
p′
11(t) = 1
4 − 5
4 p11(t).
d. Solve this equation to compute p11(t)
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