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...Markov chains sometimes we are interested in how a random variable changes over time for example may want to know the price of share stock or rm s market evolves study includes stochastic processes which ex plained this chapter particular focus on type process known as chain have been applied areas such education marketing health services nance accounting and production begin by dening concept sto chastic rest will discuss basic ideas needed an un derstanding what is suppose observe some characteristic system at discrete points labeled let x be value t most situations not with certainty before viewed simply description relation between variables examples follow gambler ruin i times play game bet probabil ity p win probability lose my goal increase capital soon do also if cap ital reduced dene position after any played then note that constant but later all equal similarly obvious reasons situation called problem choosing balls from urn contains two unpainted present choose ball ip coin ...