3 votes
Accepted

Coin flipping (Markov chain)

You are making it more complicated than it needs to be. The transition probabilities are $$P = \begin{bmatrix} 0.7 & 0.3 \\ 0.6 & 0.4 \end{bmatrix}$$ Because from the first coin there's a 70 % ...
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  • 759
2 votes

What is the influence of initial state in sequence generated from a markov chain?

To obtain the transition matrix of the Markov chain, you just observe all the transitions many times and then compute the belonging transition frequencies which are the approximations for the ...
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  • 6,633
1 vote
Accepted

How to use Stirling's formula of n! in this probability computations in random walk?

I presume that you rather want to show: $$ \frac{(2n)!}{n!n!} \sim \frac{4^n}{\sqrt{n\pi}}\tag{1}. $$ Applying Stirling we have: $$ \begin{align} \frac{(2n)!}{n!n!} &\sim \frac{(2n)^{(2n + \frac12)...
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  • 6,633
1 vote

Why not just run a Markov chain to get stationary probabilities?

In theory, some Markov chains will not have a stationary distribution. Hence, using theoretical approaches deriving the stationary distribution from the transition matrix itself should identify this ...
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  • 446

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