An extremal problem related to probability |
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Authors: | Jürg Rätz Dennis Russell |
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Institution: | (1) Mathematisches Institut der Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland;(2) Department of Mathematics, York University, M3J 1P3 Downsview, Ont., Canada |
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Abstract: | Summary We consider a walk from a stateA
1 to a stateA
n+1 in which the probability of remaining atA
i
isp
i
, and the probability of progressing fromA
i
toA
i+1 is 1 –p
i
. The probabilityW
nk
of reachingA
n+1 fromA
1 in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp
1, ,p
n
. We determine the maximum value ofW
nk
and the (unique) choice (p
1, ,p
n
) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday |
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Keywords: | Primary 26C05 Secondary 60C05 39A70 |
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