exercise:747881379d: 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 task described in Exercise Exercise, it can be shown<ref group="Notes" >E. B. Dynkin and A. A. Yushkevich, ''Markov Processes: Theorems and Problems,'' trans. J. S. Wood (New York: Plenum, 1969).</ref> that the bes...") |
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For the task described in [[exercise:C48b5291ef |Exercise]], it can be shown<ref group="Notes" >E. B. Dynkin and A. A. Yushkevich, ''Markov Processes: Theorems and Problems,'' trans. J. S. Wood (New York: Plenum, 1969).</ref> that the best strategy is | |||
be shown<ref group="Notes" >E. B. Dynkin and A. A. Yushkevich, ''Markov Processes: Theorems | |||
and Problems,'' trans. J. S. Wood (New York: Plenum, 1969).</ref> that the best strategy is | |||
to pass over the first <math>k - 1</math> candidates where <math>k</math> is the smallest integer for which | to pass over the first <math>k - 1</math> candidates where <math>k</math> is the smallest integer for which | ||
Latest revision as of 22:55, 12 June 2024
For the task described in Exercise, it can be shown[Notes 1] that the best strategy is to pass over the first [math]k - 1[/math] candidates where [math]k[/math] is the smallest integer for which
[[math]]
\frac 1k + \frac 1{k + 1} + \cdots + \frac 1{n - 1} \leq 1\ .
[[/math]]
Using this strategy the probability of getting the best candidate is approximately [math]1/e = .368[/math]. Write a program to simulate Barbara Smith's interviewing if she uses this optimal strategy, using [math]n = 10[/math], and see if you can verify that the probability of success is approximately [math]1/e[/math].
Notes