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Normal distribution: Difference between revisions
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Independent events fit nicely to a bell curve, as the [[quincunx]] pictured, likes to demonstrate. Bell curves confidently prescribe [[standard deviation]]s, probability intervals, and allow one the comfort to say, “the odds of ''x'' are such that one wouldn’t expect it in several lives of the universe”. When ''x'' really is an independent event (or a series of them) this is prudent enough: “the odds of flipping a coin and getting 99 consecutive heads is ''0.5 x 10<sup>99</sup>'', which you wouldn’t expect in several lifetimes of the universe.” | Independent events fit nicely to a bell curve, as the [[quincunx]] pictured, likes to demonstrate. Bell curves confidently prescribe [[standard deviation]]s, probability intervals, and allow one the comfort to say, “the odds of ''x'' are such that one wouldn’t expect it in several lives of the universe”. When ''x'' really is an independent event (or a series of them) this is prudent enough: “the odds of flipping a coin and getting 99 consecutive heads is ''0.5 x 10<sup>99</sup>'', which you wouldn’t expect in several lifetimes of the universe.” | ||
Then those | Then those “[[ten sigma event|ten-sigma” events]] — like, ooooh, say the correlation of a Russian government default with a spike in the price of all other G20 Treasury securities, just to pick something at random — that should, in the world of normal distributions, happen only once in every 10<sup>24</sup> times — say, ten million years — but, since investment decisions are not even remotely independent events, happened once— and only needed to happen once, to blow [[Long Term Capital Management]] and much of the market to smithereens — in ''four'' years. | ||
{{sa}} | {{sa}} | ||
*[[Social proof]]the figures implied that it would take a so-called ten-sigma event—that is, a statistical freak occurring —for the firm to lose all of its capital within one year. | *[[Social proof]]the figures implied that it would take a so-called ten-sigma event—that is, a statistical freak occurring —for the firm to lose all of its capital within one year. | ||