Is it possible to find the mean or center of a continuous arbitrary distribution. Assuming that an object O is arbitrarily distributed within arbitrary shape, can we find its mean or center geometrically or by any other method if the distribution is not known in advance.
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1Can we find the center of some random thing we know nothing about? Err... I don't think continuity is enough here. – Patrick Da Silva Apr 27 '12 at 01:51
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Can mean of an arbitrary object lies at the boundary of that object? – shaikh Apr 27 '12 at 02:03
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3Some distributions don't have means. For example, the Cauchy distribution whose density is $(1/\pi)/(1+x^2)$. – Michael Hardy Apr 27 '12 at 02:44
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@shaikh: Yes. For example, the center of mass of a line segment lies on its boundary. – Mechanical snail Nov 28 '12 at 09:54