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bouchra alami

Probability theory - Wikipedia, the free encyclopedia - 0 views

  • Probability theory is the branch of mathematics concerned with analysis of random phenomena.[1] The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Although an individual coin toss or the roll of a die is a random event, if repeated many times the sequence of random events will exhibit certain statistical patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
    • bouchra alami
       
      This is my first try with taging in Diigo. Important to know anyway :)
  • foundation
Truman Deeb

Intrinsic random event - Wikipedia, the free encyclopedia - 0 views

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    young einstein vs. old einstein why he changed his mind!
John Muccini

xkcd - A Webcomic - Random Number - 0 views

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    lol, that was clever.
Matthew Leingang

Illustrating Bertrand's Paradox with GeoGebra | Matthew Leingang - 0 views

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    I spiffed up and posted the GeoGebra worksheet if you're interested.
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    Bertrand's Paradox is a question in continuous probability that shows the perils of uniformly distributed variables. The question is simple: given a random chord in a circle, what's the probability that it's longer than the side length of an equilateral triangle inscribed in that circle?
Matthew Leingang

Bertrand's paradox (probability) - Wikipedia, the free encyclopedia - 0 views

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    What's the length of a random chord in a circle? It turns out that even if you try to distribute the chord uniformly there is an ambiguity.
Matthew Leingang

Lifelong debunker takes on arbiter of neutral choices - 0 views

  • A decade later, in 2002, a large manufacturer of card-shuffling machines for casinos summoned Diaconis to determine whether their new automated shufflers truly randomized the deck. (They didn't.)
    • Matthew Leingang
       
      I saw him talk about this. It was fascinating, especially when you consider that the problem is computationally very hard. The number of "shuffles" (permutations of a 52-card deck) exceeds the number of atoms in our galaxy, so it's impossible to build a computer with that much memory.
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    A biography about magician-turned-mathematician (probabilist) Persi Diaconis as well as a look at his experiments to understand the bias of a coin flip.
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    Great article. Everything I've been saying about Diaconis I learned through oral tradition. It's good to know I was pretty much right on.
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    Funny, after reading the article I concluded that you must've either read this article or a similar biographical sketch. Diaconis must be some legend! One of my favorite parts was that he was a bit 'rough' at one point. Gives the rest of us some hope!
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