From dc5cb2c9b65707e4cc0b516eaa65493dec9340d6 Mon Sep 17 00:00:00 2001 From: Mark Date: Thu, 26 Sep 2024 09:25:14 -0700 Subject: [PATCH] Final edits --- Advanced/Stopping Problems/parts/3 orderstat.tex | 9 +++------ 1 file changed, 3 insertions(+), 6 deletions(-) diff --git a/Advanced/Stopping Problems/parts/3 orderstat.tex b/Advanced/Stopping Problems/parts/3 orderstat.tex index 017ec1f..6a376ca 100644 --- a/Advanced/Stopping Problems/parts/3 orderstat.tex +++ b/Advanced/Stopping Problems/parts/3 orderstat.tex @@ -88,7 +88,7 @@ Given some $y$, what is the probability that all five $\mathcal{X}_i$ are smalle Say we have a random variable $\mathcal{X}$ which we observe $n$ times. \note{(for example, we repeatedly roll a die)} We'll arrange these observations in increasing order, labeled $x_1 < x_2 < ... < x_n$. \par Under this definition, $x_i$ is called the \textit{$i^\text{th}$ order statistic}---the $i^\text{th}$ smallest sample of $\mathcal{X}$. - +a \problem{} Say we have a random variable $\mathcal{X}$ uniformly distributed on $[0, 1]$, of which we take $5$ observations. \par @@ -188,10 +188,6 @@ reject the first $e^{-1} \times n$ candidates, and select the next \say{best-yet How effective is this strategy for the ranked secretary problem? \par Find the expected rank of the applicant we select using this strategy. -\begin{solution} - Coming soon. -\end{solution} - \vfill @@ -200,7 +196,8 @@ Assuming we use the same kind of strategy as before (reject $k$, select the next show that $k = \sqrt{n}$ optimizes the expected rank of the candidate we select. \begin{solution} - This is a difficult bonus problem. Solution coming later. + This is a difficult bonus problem. see + \texttt{Neil Bearden, J. (2006). A new secretary problem with rank-based selection and cardinal payoffs.} \end{solution} \vfill