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 | \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 | |||
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.)