Normal distribution: Difference between revisions

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{{a|systems|{{file|Quincunx|jpg|Some independent events, yesterday]]}}A [[normal distribution]]<ref>Also called a “[[Gaussian]]” distribution, after the chap who first formulated it, but only by people who are trying to sound clever.</ref> of a series of events, indicates that the events are independent of each other, in that the occurrence of one does not affect the probability of another. [[Coin flip]]s are independent of each other. So are rolls of a die, or the distribution of heights in a classroom. Homo sapiens being the fickle, [[social proof|biddable]] species it is, its cognitive decisions — particularly those concerning [[fashionable idea]]s, to depart quickly from crowded theatres when someone yells fire or to hysterically buy, and then sell, [[Enron]] stock ''[[for fear of missing out]]'' — are not.
{{a|systems|{{image|Quincunx|jpg|Some independent events, yesterday}}}}A [[normal distribution]]<ref>Also called a “[[Gaussian]]” distribution, after the chap who first formulated it, but only by people who are trying to sound clever.</ref> of a series of events, indicates that the events are independent of each other, in that the occurrence of one does not affect the probability of another. [[Coin flip]]s are independent of each other. So are rolls of a die, or the distribution of heights in a classroom. Homo sapiens being the fickle, [[social proof|biddable]] species it is, its cognitive decisions — particularly those concerning [[fashionable idea]]s, to depart quickly from crowded theatres when someone yells fire or to hysterically buy, and then sell, [[Enron]] stock ''[[for fear of missing out]]'' — are not.
===Independent events===
===Independent events===
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.”