2.12 Two urns contain k balls each. Initially, the balls in the left urn are all red and the balls in the right urn are all blue. At each step, pick a ball at random from each urn and exchange them. Let X, be the number of blue balls in the left urn. (Note that necessarily Xo = 0 and X, = 1.) Argue that the process is a Markov chain. Find the transition matrix. This model is called the Bernoulli-Laplace model of diffusion and was introduced by Daniel Bernoulli in 1769 as a model for the flow of two incompressible liquids between two containers. %3D
2.12 Two urns contain k balls each. Initially, the balls in the left urn are all red and the balls in the right urn are all blue. At each step, pick a ball at random from each urn and exchange them. Let X, be the number of blue balls in the left urn. (Note that necessarily Xo = 0 and X, = 1.) Argue that the process is a Markov chain. Find the transition matrix. This model is called the Bernoulli-Laplace model of diffusion and was introduced by Daniel Bernoulli in 1769 as a model for the flow of two incompressible liquids between two containers. %3D
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.6P
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![2.12 Two urns contain k balls each. Initially, the balls in the left urn are all red and
the balls in the right urn are all blue. At each step, pick a ball at random from
each urn and exchange them. Let X, be the number of blue balls in the left urn.
(Note that necessarily X, = 0 and X, = 1.) Argue that the process is a Markov
chain. Find the transition matrix. This model is called the Bernoulli-Laplace
model of diffusion and was introduced by Daniel Bernoulli in 1769 as a model
for the flow of two incompressible liquids between two containers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95091e31-aa59-4ab3-abd1-ef0a359ae915%2F1dee01f1-39ab-43ac-974f-ff591f2cf3b5%2Fzf4ggd7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.12 Two urns contain k balls each. Initially, the balls in the left urn are all red and
the balls in the right urn are all blue. At each step, pick a ball at random from
each urn and exchange them. Let X, be the number of blue balls in the left urn.
(Note that necessarily X, = 0 and X, = 1.) Argue that the process is a Markov
chain. Find the transition matrix. This model is called the Bernoulli-Laplace
model of diffusion and was introduced by Daniel Bernoulli in 1769 as a model
for the flow of two incompressible liquids between two containers.
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