# Tagged Questions

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### A Markov Chain Problem.(Change the color of ball)

There are $n$ different color balls in a box. Take two balls in turns, and change color of the second ball to the first. (This is one operation). Let $k$ be the (random) number of operations needed to ...
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### Prove this is markov chain [on hold]

Let $Y_i = i$ with probability $p_i$. Let $X_i = max[Y_i , Y_i-1, ...].$ We have $i={0,1,2,3,4,...}.$ Prove that $X_i$ is a Markov chain and write down its matrix.
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### How to apply the strong Markov property in this case?

I'm trying to understand the following proof: Theorem: Let $(X_n)$ be an irreducible $(\alpha, \mathbf p)$-Markov chain with a finite state space $S$. Then $(X_n)$ is positive recurrent. ...
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### Max of independent and identical random variables is Markov

I'm supposed to show that given a sequence $\{Y_n\}$ of i.i.d the stochastic process $$X_n=\max(Y_0, Y_1...,Y_n)$$ is a Markov of chain. I think I could do it by induction but I would rather see how ...
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### A question about a Markov Chain

I encountered a question about Markov Chains which looks interesting. Given a homogeneous, irreducible, non cyclic Markov Chain with $K$ possible states and a transition matrix $Q$. We define $T_i$ ...
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### Supply the transition matrix for these (possible) Markov chains

Reading Grimmet, Stirzaker: Probability and Random Processes, which unfortunately doesn't have solutions. Trying to make sure I understand Markov chains. A die is rolled repeatedly. Which of these ...
I am reading a paper on Markov Models and I am trying to figure out how to compute the probabilities for the $\alpha$-pass. I am given an $N\times N$ matrix $A$, that has the probabilities of ...