Problem 3 We consider a group of 4 students among which a rumour is spreading. At time 0, only one student is aware of the rumour. Whenever two students meet, if one is aware of the rumour and not the other, the second one becomes aware of it. We assume that for any pair of students, the times at which they meet forms a Poisson process with rate 1. We also assume that, for the 6 possible pairs of students, we get 6 independent Poisson processes. a. Let A(t) be the number of students aware of the rumour at time t. We admit this is a continuous- time Markov chain. Give its parameters. No proof is required. b. Let T be the first time at which all students become aware of the rumour. Compute E[T].
Problem 3 We consider a group of 4 students among which a rumour is spreading. At time 0, only one student is aware of the rumour. Whenever two students meet, if one is aware of the rumour and not the other, the second one becomes aware of it. We assume that for any pair of students, the times at which they meet forms a Poisson process with rate 1. We also assume that, for the 6 possible pairs of students, we get 6 independent Poisson processes. a. Let A(t) be the number of students aware of the rumour at time t. We admit this is a continuous- time Markov chain. Give its parameters. No proof is required. b. Let T be the first time at which all students become aware of the rumour. Compute E[T].
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 3
We consider a group of 4 students among which a rumour is spreading. At time 0, only one student
is aware of the rumour. Whenever two students meet, if one is aware of the rumour and not the
other, the second one becomes aware of it. We assume that for any pair of students, the times at
which they meet forms a Poisson process with rate 1. We also assume that, for the 6 possible pairs
of students, we get 6 independent Poisson processes.
a. Let A(t) be the number of students aware of the rumour at time t. We admit this is a continuous-
time Markov chain. Give its parameters. No proof is required.
b. Let T be the first time at which all students become aware of the rumour. Compute E[T].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ce6fdd3-7319-4b16-8948-2d2b1b56e05e%2F789b5ec1-45c2-4dba-acd2-c3b829e2f1cd%2Ffy2zrii_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3
We consider a group of 4 students among which a rumour is spreading. At time 0, only one student
is aware of the rumour. Whenever two students meet, if one is aware of the rumour and not the
other, the second one becomes aware of it. We assume that for any pair of students, the times at
which they meet forms a Poisson process with rate 1. We also assume that, for the 6 possible pairs
of students, we get 6 independent Poisson processes.
a. Let A(t) be the number of students aware of the rumour at time t. We admit this is a continuous-
time Markov chain. Give its parameters. No proof is required.
b. Let T be the first time at which all students become aware of the rumour. Compute E[T].
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