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Month: November 2020

Rejection sampling, order statistics, and Dungeons and Dragons

November 19, 2020 Joseph Deutsch 2 Comments

$\newcommand{\E}{\operatorname{E}}\newcommand{\Xmin}{X_{(1)}}\newcommand{\Fmin}{F_{(1)}}\newcommand{\fmin}{f_{(1)}}\newcommand{\eff}{\operatorname{eff}}$In this post I’m going to look at two probability questions that arose in the context of a friendly game…

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Posted in: Probability

Evaluating $\lim_{n\to\infty} (n!)^{1/n}$

November 12, 2020 Joseph Deutsch Leave a comment

$\newcommand{\R}{\mathbb R}\newcommand{\N}{\mathbb N}$In this post I’m going to evaluate $$ \lim_{n\to\infty} (n!)^{1/n} $$ by connecting it to the harmonic series.…

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Posted in: Real analysis

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  • Changing $y$ without changing $\hat\beta$ and $\hat\sigma^2$ in linear regression
  • Clique counting and The Twelve Days of Christmas
  • The degree distribution of the stochastic block model
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