exercise:B6a9291017: 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> A certain calculating machine uses only the digits 0 and 1. It is supposed to transmit one of these digits through several stages. However, at every stage, there is a probability <math>p</math> that the digit that enters this stage will be chang...") |
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\newcommand{\mathds}{\mathbb}</math></div> A certain calculating machine uses only the digits | \newcommand{\mathds}{\mathbb}</math></div> A certain calculating machine uses only the digits 0 and 1. It is supposed to transmit one of these digits through several stages. However, at every stage, there is a probability <math>p</math> that the digit that enters this stage will be changed when it leaves and a probability <math>q = 1 - p</math> that it won't. Form a Markov chain to represent the process of transmission by taking as states the digits 0 and 1. What is the matrix of transition probabilities? | ||
0 and 1. It is supposed to transmit one of these digits through several | |||
stages. However, at every stage, there is a probability <math>p</math> that the digit | |||
that | |||
enters this stage will be changed when it leaves and a probability <math>q = 1 - p</math> | |||
that it won't. Form a Markov chain to represent the process of transmission by | |||
taking as states the digits 0 and 1. What is the matrix of transition | |||
probabilities? | |||
Latest revision as of 00:18, 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]
A certain calculating machine uses only the digits 0 and 1. It is supposed to transmit one of these digits through several stages. However, at every stage, there is a probability [math]p[/math] that the digit that enters this stage will be changed when it leaves and a probability [math]q = 1 - p[/math] that it won't. Form a Markov chain to represent the process of transmission by taking as states the digits 0 and 1. What is the matrix of transition probabilities?