I've got a box with 10 balls inside, 5 reds 5 blacks. Every step i take a ball. If it is black i hold it out, if it is red i put all the blacks ball that are out and the red one inside the box. Called $X_{n}$ the number of balls that are outside the box at the n° step, prove that $X_n$ is a markov chain.
Demonstrate that is a Markov Chain
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0Since this is homework, please edit to show what you have done so far. What part of the definition of a Markov chain are you having trouble verifying? – 2012-01-13
1 Answers
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It is a Markov chain because the distribution of $X_{n+1}$ depends only on the observation of $X_{n}$ because the number of balls outside of the box completely determines the state of the system at any given step.
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0ok, that's right but my problem is that i don't know how to prove that in a "formal way": i thought that $X_{n}=(i+1)Y_{n}$ where $X_{n-1}=i$ and $Y_{n}$ goes like a $B(1,\frac{5-i}{10-i})$ but i don't know how to end. Maybe I'm drowning in an inch of water, but I'm not so sure about it. – 2019-01-30