Markov Chains; what exactly are they?
<p>Markov chains, a powerful tool in probability, yet a hated course at university. As arguably one of the most controversial areas in probability, in this post we look into the journey of Markov chains. Any part marked with<strong> (**) </strong>should be attempted by the reader.</p>
<p>This is best illustrated by an example, before getting into any theory. Suppose that we had a very basic problem as follows.<br />
<strong>(**) </strong>A frog hops between two lily pads. Each minute it has a probability of 2/3 to hop onto the other lily pad, with a probability of 1/3 to stay in place. What is the probability that after n minutes, it is on the lily pad that it started on?</p>
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