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almostsuremath.com | ||
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jmanton.wordpress.com
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| | | | | If $latex Y$ is a $latex \sigma(X)$-measurable random variable then there exists a Borel-measurable function $latex f \colon \mathbb{R} \rightarrow \mathbb{R}$ such that $latex Y = f(X)$. The standard proof of this fact leaves several questions unanswered. This note explains what goes wrong when attempting a "direct" proof. It also explains how the standard proof... | |
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thatsmaths.com
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| | | | | We consider a simple problem in probability: A thin rod is broken at random into three pieces. What is the probability that these three pieces can be used to form a triangle? This problem is solved without difficulty. If the rod is of unit length, aligned along the interval $latex {0\le x \le 1}&fg=000000$, we... | |
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www.randomservices.org
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| | | | | [AI summary] The text covers various topics in probability and statistics, including continuous distributions, empirical density functions, and data analysis. It discusses the uniform distribution, rejection sampling, and the construction of continuous distributions without probability density functions. The text also includes data analysis exercises involving empirical density functions for body weight, body length, and gender-specific body weight. | |
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chava61photography.photo.blog
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