A group of enthusiastic investors open brokerage accounts and decide to purchase either stocks or bonds every trading day. The investors' daily choice of assets can be modeled by a Markov chain: 75% of the investors who bought stocks today will buy stocks tomorrow, and 70% of the investors who bought bonds today will buy bonds tomorrow. (a) Write down the stochastic matrix corresponding to this Markov chain. (b) In the long run, what proportion of the investors each trading day will buy bonds?

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