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The article doesn't share the actual math, but also not the relatively easy intuition. When you roll a pair of dice, there are more combinations that add up to
by bux93 7mo ago
The article doesn't share the actual math, but also not the relatively easy intuition. When you roll a pair of dice, there are more combinations that add up to 7 than any other number. Change the numbers on the dice (change the 1 to a 6, e.g.), there's again more combinations that add up to some numbers than to others. The histogram of the number of combinations that add up to different results is a bell curve. That's why it pops up everywhere you have addition of independent events.
It's sad that even introductory statistics courses skip this simple intuition.
- cortesoft 7mo agoAnybody who has ever played Craps will know this.
- AlexCornila 7mo agoYeah that is definitely not the relatively easy intuition for this. The relatively easy intuition comes from learning about the Bernoulli trials, binomial distribution and Pascal triangle. Once you understand those you understand why normal distribution is so prevalent. Or just watch this https://youtu.be/AwEaHCjgeXk?si=tV72uauquCHvzkNE https://youtu.be/AwEaHCjgeXk?si=tV72uauquCHvzkNE
- estearum 7mo agoThey explained the intuition in like two sentences that an 8th grader can understand and test themselves. Sounds simpler than whatever you’re talking about here
- trymas 7mo ago> It's sad that even introductory statistics courses skip this simple intuition. I was probably lucky. We got homework as one of the first lessons in statistics course, for exactly this case. Roll pair of dice, save the result, do it 200 (or some other bigger number) times, plot the histogram, do some maths, maybe provide any conclusions, etc. Such things then definitely stuck with you for a long time.
- srean 7mo agoAnd if you take the log of the number of ways you get the entropy corresponding to the 'ways' macrostate.
- streptomycin 7mo agoThe distribution of the sum of two dice is actually triangular, not a bell curve https://math.stackexchange.com/a/1204492 https://math.stackexchange.com/a/1204492
- mr_toad 7mo agoThe distribution of the sum of a finite number of dice only approximates a bell curve. https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distributio...