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Lentil convexity: Difference between revisions
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But the peacetime lentil-buying motivations of a hippy, a vegetarian and the proverbial meat-and-potatoes munching, Clapham omnibus-riding ordinary fellow are quite distinct, and unrelated. Each person’s decisions are, within a fairly tight range, predictable and and independent of each other: ''my'' lentil acquisition does not greatly influence, and is not particularly correlated with, ''yours''. | But the peacetime lentil-buying motivations of a hippy, a vegetarian and the proverbial meat-and-potatoes munching, Clapham omnibus-riding ordinary fellow are quite distinct, and unrelated. Each person’s decisions are, within a fairly tight range, predictable and and independent of each other: ''my'' lentil acquisition does not greatly influence, and is not particularly correlated with, ''yours''. | ||
National weekly lentil purchases therefore usually cleave to a [[normal distribution]]. A small part of the population (say 0.5% | National weekly lentil purchases therefore usually cleave to a [[normal distribution]]. A small part of the population (say 0.5% — the hippies) may buy 8, 9 or 10 tins. A larger part (say 4.5% — vegans, health-food fanatics etc.) may buy one or two, and the remaining 95% will buy very few (let’s say on average 0.1 tin each: one tin between ten, which is probably generous). Since lentil buyers’ decisions are unconnected — that each lentil tin acquisition is an ''independent'' event<ref>BUT IS IT. I don’t want to spoil the punchline but HOLD THAT THOUGHT.</ref> — it all tends to even out, within a range. Each of these numbers will fluctuate, week to week, but in the same week that your hippie stocks up extra for his bom shankar summer solstice druid’s convention cauldron ''partay'', your vegan might skip a tin, and your 95% who hardly ever buy lentils make little difference to the acquisition rate in any weather. | ||
The odds of ''everyone'', including the normals, ''all'' going large on lentils ''in the same week'' is extremely low.<ref>With genuinely unconnected events the probabilities fade into cosmic radiation fast: the odds of tossing heads just 100 times in a row with a fair coin is one in ''half a googol''. If it takes ten minutes to toss 100 times, you wouldn’t expect it to happen in ''several lives of the universe''.</ref> The consequence, across the community, is a [[normal distribution]] of weekly lentil acquisition. The random variation in purchases by people in the different demographic groups will cause a small fluctuation in in demand for lentils from week to week, but from a grocer’ perspective, the demand curve is predictable and manageable. | The odds of ''everyone'', including the normals, ''all'' going large on lentils ''in the same week'' is extremely low.<ref>With genuinely unconnected events the probabilities fade into cosmic radiation fast: the odds of tossing heads just 100 times in a row with a fair coin is one in ''half a googol''. If it takes ten minutes to toss 100 times, you wouldn’t expect it to happen in ''several lives of the universe''.</ref> The consequence, across the community, is a [[normal distribution]] of weekly lentil acquisition. The random variation in purchases by people in the different demographic groups will cause a small fluctuation in in demand for lentils from week to week, but from a grocer’ perspective, the demand curve is predictable and manageable. | ||