exercise:8f7de90f5a: 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> For the Markov chain in Exercise Exercise, draw a tree and assign a tree measure assuming that the process begins in state 0 and moves through two stages of transmission. What is the probability that the machine, after t...") |
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For the Markov chain in [[exercise:B6a9291017 |Exercise]], draw a tree and assign a tree measure assuming that the process begins in state 0 and moves through two stages of transmission. What is the probability that the machine, after two stages, produces the digit 0 (i.e., the correct digit)? What is the probability that the machine never changed the digit from 0? Now let <math>p = .1</math>. | |||
Using the program ''' MatrixPowers''', compute the 100th power of the transition matrix. | |||
a tree | |||
and assign a tree measure assuming that the process begins in state 0 and moves | |||
through | |||
two stages of transmission. What is the probability that the machine, after | |||
two | |||
stages, produces the digit 0 (i.e., the correct digit)? What is the | |||
probability that the machine never changed the digit from 0? Now let <math>p = .1</math>. | |||
Using | |||
the program ''' MatrixPowers''', compute the 100th power of the transition | |||
matrix. | |||
Interpret the entries of this matrix. Repeat this with <math>p = .2</math>. Why do the | Interpret the entries of this matrix. Repeat this with <math>p = .2</math>. Why do the | ||
100th | 100th powers appear to be the same? | ||
powers appear to be the same? | |||
Latest revision as of 00:19, 15 June 2024
For the Markov chain in Exercise, draw a tree and assign a tree measure assuming that the process begins in state 0 and moves through two stages of transmission. What is the probability that the machine, after two stages, produces the digit 0 (i.e., the correct digit)? What is the probability that the machine never changed the digit from 0? Now let [math]p = .1[/math]. Using the program MatrixPowers, compute the 100th power of the transition matrix. Interpret the entries of this matrix. Repeat this with [math]p = .2[/math]. Why do the 100th powers appear to be the same?