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thatsmaths.com | ||
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mkatkov.wordpress.com
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| | | | | For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... | |
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sriku.org
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| | | | | [AI summary] The article explains how to generate random numbers that follow a specific probability distribution using a uniform random number generator, focusing on methods involving inverse transform sampling and handling both continuous and discrete cases. | |
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hbfs.wordpress.com
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| | | | | $latex n!$ (and its logarithm) keep showing up in the analysis of algorithm. Unfortunately, it's very often unwieldy, and we use approximations of $latex n!$ (or $latex \log n!$) to simplify things. Let's examine a few! First, we have the most known of these approximations, the famous "Stirling formula": $latex \displaystyle n!=\sqrt{2\pi{}n}\left(\frac{n}{e}\right)^n\left(1+\frac{1}{12n}+\frac{1}{288n^2}-\frac{139}{51840n^3}-\cdots\right)$, Where the terms... | |
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ddarmon.github.io
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