Art of the Problem on MSN
From Plato to Markov chains, how probability revealed hidden patterns in random events
From Plato’s search for hidden forms to Bernoulli’s law of large numbers and Markov’s breakthrough on dependent events, this story traces how mathematicians discovered the patterns hidden inside ...
A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...
Imagine examining the first 20,000 letters of a book, counting frequencies and studying patterns. This is precisely what Andrey Markov did when he analysed the text of Alexander Pushkin's verse novel ...
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