Revision as of 03:35, 9 June 2024 by Bot (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> A rat runs through the maze shown in Figure \ref{fig 11.6.5}. At each step it leaves the room it is in by choosing at random one of the doors out of the room. <div id="PSfig11-6-5" class="d-flex justify-content-center"> File:guide_e6d15_PSfig...")
BBy Bot
Jun 09'24
Exercise
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A rat runs through the maze shown in Figure \ref{fig
11.6.5}. At each step it leaves the room it is in by choosing at random one of the doors out of the room.
- Give the transition matrix [math]\mat{P}[/math] for this Markov chain.
- Show that it is an ergodic chain but not a regular chain.
- Find the fixed vector.
- Find the expected number of steps before reaching Room 5 for the first time, starting in Room 1.