exercise:7ce803dbdf: 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> In Monte Carlo roulette (see Example), under option (c), there are six states (<math>S</math>, <math>W</math>, <math>L</math>, <math>E</math>, <math>P_1</math>, and <math>P_2</math>). The reader is referred to Fi...") |
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\newcommand{\mathds}{\mathbb}</math></div> In Monte Carlo roulette (see | \newcommand{\mathds}{\mathbb}</math></div> In Monte Carlo roulette (see [[guide:E4fd10ce73#exam 6.1.5 |Example]]), under option (c), there are six states (<math>S</math>, <math>W</math>, <math>L</math>, <math>E</math>, <math>P_1</math>, and <math>P_2</math>). The reader is referred to [[guide:E4fd10ce73#fig 6.1.5|Figure]], which contains a tree for this option. Form a Markov chain for this option, and use the program '''AbsorbingChain''' to find the probabilities that you win, lose, or break even for a 1 franc bet on red. Using these probabilities, find the expected winnings for this bet. For a more general discussion of Markov chains applied to roulette, see the article of H. Sagan referred to in [[guide:E4fd10ce73#exam 6.7|Example]]. | ||
[[guide:E4fd10ce73#exam 6.1.5 |Example]]), | |||
under option (c), there are six states (<math>S</math>, <math>W</math>, <math>L</math>, <math>E</math>, <math>P_1</math>, and <math>P_2</math>). | |||
The reader | |||
is referred to | |||
Form | |||
a Markov chain for this option, and use the program ''' AbsorbingChain''' to | |||
find the | |||
probabilities that you win, lose, or break even for a 1 franc bet on red. | |||
Using these | |||
probabilities, find the expected winnings for this bet. | |||
discussion of | |||
Markov chains applied to roulette, see the article of H. Sagan referred to in | |||
[[guide:E4fd10ce73#exam 6.7 |Example]]. | |||
Latest revision as of 01:22, 16 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]
In Monte Carlo roulette (see Example), under option (c), there are six states ([math]S[/math], [math]W[/math], [math]L[/math], [math]E[/math], [math]P_1[/math], and [math]P_2[/math]). The reader is referred to Figure, which contains a tree for this option. Form a Markov chain for this option, and use the program AbsorbingChain to find the probabilities that you win, lose, or break even for a 1 franc bet on red. Using these probabilities, find the expected winnings for this bet. For a more general discussion of Markov chains applied to roulette, see the article of H. Sagan referred to in Example.