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Cyan comments on A Request for Open Problems - Less Wrong
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"The uniform distribution centered at c" does not seem to make sense. Did you perchance mean the Gaussian distribution? Further, 'deviates' looks like jargon to me. Can we use 'samples'? I would therefore rephrase as follows, with specific example to hang one's visualisation on:
Heights of male humans are known to have a Gaussian distribution of width 10 cm around some central value <h>; unfortunately you have forgotten what the central value is. Joe is 180 cm, Stephen is 170 cm. The probability that <h> is between these two heights is 50%; explain why. Then find a better confidence interval for <h>.
I mean the continuous uniform distribution. "Centered at c" is intended to indicate that the mean of the distribution is c.
ETA: Let me be specific -- I'll use the notation of the linked Wikipedia article.
You know that b - a = 1.
c = (a + b)/2 is unknown, and the confidence interval is supposed to help you infer it.