exercise:A86a5bb531: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Three tanks fight a three-way duel. Tank A has probability 1/2 of destroying the tank at which it fires, tank B has probability 1/3 of destroying the tank at which it fires, and tank C has probability 1/6 of destroying the tank at which it fir...") |
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\newcommand{\mathds}{\mathbb}</math></div> Three tanks fight a three-way duel. Tank A has | \newcommand{\mathds}{\mathbb}</math></div> Three tanks fight a three-way duel. Tank A has probability 1/2 of destroying the tank at which it fires, tank B has probability 1/3 of destroying the tank at which it fires, and tank C has probability 1/6 of destroying the tank at which it fires. The tanks fire together and each tank fires at the strongest opponent not yet destroyed. Form a Markov chain by taking as states the subsets of the set of tanks. Find <math>\mat{N},~\mat{N}\mat{c}</math>, and <math>\mat{N}\mat{R}</math>, and interpret your results. '' Hint'': Take as states ABC, AC, BC, A, B, C, and none, indicating the tanks that could survive starting in state ABC. You can omit AB because this state cannot be reached from ABC. | ||
probability 1/2 of destroying the tank at which it fires, tank B has | |||
probability 1/3 of destroying the tank at which it fires, and tank C has | |||
probability 1/6 of destroying the tank at which it fires. The tanks fire | |||
together | |||
and each tank fires at the strongest opponent not yet destroyed. Form a Markov | |||
chain by taking as states the subsets of the set of tanks. Find | |||
<math>\mat{N},~\mat{N}\mat{c}</math>, | |||
and <math>\mat{N}\mat{R}</math>, and interpret your results. '' Hint'': | |||
Take as states ABC, AC, BC, A, B, C, and none, indicating the tanks that could | |||
survive starting in state ABC. You can omit AB because this state cannot be | |||
reached from ABC. | |||
Latest revision as of 23:22, 15 June 2024
[math]
\newcommand{\NA}{{\rm NA}}
\newcommand{\mat}[1]{{\bf#1}}
\newcommand{\exref}[1]{\ref{##1}}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}[/math]
Three tanks fight a three-way duel. Tank A has probability 1/2 of destroying the tank at which it fires, tank B has probability 1/3 of destroying the tank at which it fires, and tank C has probability 1/6 of destroying the tank at which it fires. The tanks fire together and each tank fires at the strongest opponent not yet destroyed. Form a Markov chain by taking as states the subsets of the set of tanks. Find [math]\mat{N},~\mat{N}\mat{c}[/math], and [math]\mat{N}\mat{R}[/math], and interpret your results. Hint: Take as states ABC, AC, BC, A, B, C, and none, indicating the tanks that could survive starting in state ABC. You can omit AB because this state cannot be reached from ABC.