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Model the following systems as discrete time Markov chains. Define the Markov chains by precisely stating...

Model the following systems as discrete time Markov chains. Define the Markov chains by precisely stating the quantity of interest, give the state space, draw a state diagram, and write down the one step transition probability matrix.

(a) Every evening I eat at one of my three favorite restaurants in Bruntsfield. Having eaten at a restaurant one night, the next evening I’ll go to one of the other two restaurants equally likely.

(b) Consider a special gambler’s ruin problem, where the total wealth is £5, and you play many rounds against an opponent. You win each round with probability 2/3 and then you get £1 from your opponent, otherwise you lose and you give £2 to your opponent (or £1 if you only have £1). If someone gets to own all wealth they keep that in all further rounds.

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orchestra answered 1 year ago
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