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## Main Question or Discussion Point

Hello there,

I'm stuck at a problem on markov chains... Could anyone help?

Here it is:

There are two machines that operate or don't during a day. Let $$X(n)$$ be the number of machines operating during the n-th day. Every machine is independently operating during the n-th day with probability $$\frac{1+X(n-1)}{4}$$. Show that the process $$\{ X(n):n=1,2,...\}$$ is markovian and find its transition matrix.

I'm stuck at a problem on markov chains... Could anyone help?

Here it is:

There are two machines that operate or don't during a day. Let $$X(n)$$ be the number of machines operating during the n-th day. Every machine is independently operating during the n-th day with probability $$\frac{1+X(n-1)}{4}$$. Show that the process $$\{ X(n):n=1,2,...\}$$ is markovian and find its transition matrix.