Stochastic Processes
https://www.maa.org/taxonomy/term/42058/all
enChutes and Ladders for the Impatient
https://www.maa.org/programs/maa-awards/writing-awards/chutes-and-ladders-for-the-impatient
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span style="font-size: small;"><span style="font-family: verdana,geneva;"><strong>Award:</strong> George PĆ³lya</span></span></p>
<p><span style="font-size: small;"><span style="font-family: verdana,geneva;"><span style="font-size: small;"><strong>Year of Award: </strong>2012</span></span></span></p>
<p><span style="font-size: small;"><span style="font-family: verdana,geneva;"><span style="font-size: small;"><strong>Publication Information:</strong> C<em>ollege Mathematics Journal, </em>vol. 42, no. 1, January 2011, pp. 2-8.</span></span></span></p></div></div></div>
Wed, 08 Aug 2012 18:10:45 +0000
saratt114045 at https://www.maa.orgThe Gunfight at the OK Corral
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-gunfight-at-the-ok-corral
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>This article uses a generalization of a three-way gunfight to motivate the construction and solution to a first order linear system of difference equations. The method of undetermined coefficients is used to develop a general solution to the dynamical system. Probabilities of the system converging to each final (absorbing) state are found. According to the author, many mathematical models can be approached from the point of view of discrete dynamical systems.</em></p>
</div></div></div>
Fri, 12 Jul 2013 15:03:25 +0000
newton_admin94749 at https://www.maa.orgComputing the Fundamental Matrix for a Reducible Markov Chain
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/computing-the-fundamental-matrix-for-a-reducible-markov-chain
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>A Markov chain with 9 states is used to illustrate a technique for finding the fundamental matrix.</em></p>
</div></div></div>
Fri, 12 Jul 2013 15:03:25 +0000
newton_admin95376 at https://www.maa.orgOn the Convergence of the Sequence of Powers of a \(2 \times 2\) Matrix
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-convergence-of-the-sequence-of-powers-of-a-2-times-2-matrix
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The fact that the <em>limit of the \(n\)-th power of a \(2\times 2\) matrix \(A\) tends to \(0\) if \( \det A < 1\) and \( \mid 1 + \det(A) \mid > \mid\) tr\( (A) \mid \)</em> is used to prove a well-known theorem in Markov chains for \(2 \times 2\) regular stochastic matrices and to obtain an explicit formula for the stationary matrix and eigenvector.</p>
</div></div></div>
Fri, 12 Jul 2013 15:03:25 +0000
newton_admin95406 at https://www.maa.orgA Markov Chain Analysis of the Game of Jai Alai
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-markov-chain-analysis-of-the-game-of-jai-alai
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The game of Jai Alai is used to demonstrate use of Markov chains in modeling.</em></p>
</div></div></div>
Fri, 12 Jul 2013 15:03:25 +0000
newton_admin95409 at https://www.maa.orgThe Undying Novena
https://www.maa.org/programs/faculty-and-departments/course-communities/the-undying-novena
Fri, 12 Jul 2013 15:06:16 +0000
newton_admin115292 at https://www.maa.orgDiscrete - Time Markov Chains
https://www.maa.org/programs/faculty-and-departments/course-communities/discrete-time-markov-chains
Fri, 12 Jul 2013 15:06:16 +0000
newton_admin115272 at https://www.maa.orgA Random Walk in One Dimension: Applet Demonstration
https://www.maa.org/programs/faculty-and-departments/course-communities/a-random-walk-in-one-dimension-applet-demonstration
Fri, 12 Jul 2013 15:06:16 +0000
newton_admin115273 at https://www.maa.orgMarkov Chains
https://www.maa.org/programs/faculty-and-departments/course-communities/markov-chains
Fri, 12 Jul 2013 15:06:16 +0000
newton_admin115274 at https://www.maa.orgThe Ehrenfest Chains
https://www.maa.org/programs/faculty-and-departments/course-communities/the-ehrenfest-chains
Fri, 12 Jul 2013 15:06:16 +0000
newton_admin115275 at https://www.maa.orgThe Disadvantage of Too Much Success.
https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-disadvantage-of-too-much-success
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective is to choose the success probability so as to maximise the expected reward before the stopping time applies.</em></p>
</div></div></div>
Wed, 18 Jun 2014 01:13:24 +0000
lang429891 at https://www.maa.org