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I've been asked to provide a distribution that best describes the place a dart might hit on the dart board. At first glance I though it would be uniform, but that would be true if we were talking about someone throwing it with a blindfold on, then I thought a bivariate normal distribution might do a better job, but I cannot seem to give a reasonable explanation for it.

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    $\begingroup$ I would say: radius is one-sided normal centered at $0$. Angle is uniform on $[0,2\pi]$. Or, equivalently, let the radius be normal centered at $0$ and angle uniform on $[0,\pi]$. $\endgroup$
    – lulu
    Jun 20 at 17:20
  • $\begingroup$ Your reason would be that they are trying to hit the center and don’t suck. $\endgroup$
    – Jellyfish
    Jun 20 at 17:25

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It depends on factors such as precision and accuracy. If the dart is precise but not accurate, you’ll get a bivariate normal but not at the center. If it is precise and accurate, you’ll get a bivariate normal at the center. If it’s accurate but not precise, you could get a bivariate normal with large variance, or a uniform if you wish. The same is with not accurate and not precise—the hits are centered outside the target but have large spread, so could be modeled using a bivariate normal or a uniform.

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    $\begingroup$ Spell checker is your enemy. $\endgroup$ Jun 20 at 17:45
  • $\begingroup$ Drats, I wanted to talk about bicarbonate ions. $\endgroup$
    – Jellyfish
    Jun 20 at 18:25

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