Dc^ly stochastic Markov chains Exsrcise 7.12. A man has m identical hats that he keeps in two dra...
Dc^ly stochastic Markov chains Exsrcise 7.12. A man has m identical hats that he keeps in two drawers, one fair coin in his pocket, and the following strange ritual. Each morning, he flips the coin to choose a drawer at random and take one hat from this drawer, if there is one, to wear all the day. In the evening of the days when he wears a hat, he flips again the coin to choose a drawer at random where to put the hat back. Find the fraction of days the man does not wear a hat. Hint: Introduce a Markov chain that keeps track of the hats and use the fact that the transition matrix is doubly stochastic.
Dc^ly stochastic Markov chains Exsrcise 7.12. A man has m identical hats that he keeps in two drawers, one fair coin in his pocket, and the following strange ritual. Each morning, he flips the coin to choose a drawer at random and take one hat from this drawer, if there is one, to wear all the day. In the evening of the days when he wears a hat, he flips again the coin to choose a drawer at random where to put the hat back. Find the fraction of days the man does not wear a hat. Hint: Introduce a Markov chain that keeps track of the hats and use the fact that the transition matrix is doubly stochastic.