exercise:Bc75f812c0: Difference between revisions

From Stochiki
(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> Using the result of Exercise Exercise, make a conjecture for the form of the fundamental matrix if the process moves as in that exercise, except that it now moves on the integers from 1 to <math>n</math>. Test your conj...")
 
No edit summary
 
Line 5: Line 5:
\newcommand{\secstoprocess}{\all}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}</math></div> Using the result of Exercise [[exercise:Fd190e1214 |Exercise]], make a  
\newcommand{\mathds}{\mathbb}</math></div> Using the result of [[exercise:Fd190e1214 |Exercise]], make a conjecture for the form of the fundamental matrix if the process moves as in that exercise, except that it now moves on the integers from 1 to <math>n</math>.  Test your conjecture for several different values of <math>n</math>.  Can you conjecture an estimate for the expected number of steps to reach state <math>n</math>, for large <math>n</math>?  (See [[exercise:0605c203bb|Exercise]] for a method of determining this expected number of steps.)
conjecture for the form of the fundamental matrix if the process moves as in
that  
exercise, except that it now moves on the integers from 1 to <math>n</math>.  Test your
conjecture for several different values of <math>n</math>.  Can you conjecture an estimate
for the expected number of steps to reach state <math>n</math>, for large <math>n</math>?  (See  
Exercise \ref{exer 11.2.10.5} for a method of determining this expected number
of
steps.)

Latest revision as of 22:12, 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]

Using the result of Exercise, make a conjecture for the form of the fundamental matrix if the process moves as in that exercise, except that it now moves on the integers from 1 to [math]n[/math]. Test your conjecture for several different values of [math]n[/math]. Can you conjecture an estimate for the expected number of steps to reach state [math]n[/math], for large [math]n[/math]? (See Exercise for a method of determining this expected number of steps.)