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Stephen Tashi

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If you assume a distribution that is spherically symmetric about (0,0,0) in each shell, the expected coordinates of the object will be (0,0,0).

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Stephen Tashi

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Compute the volume v_i of each shell i = 1,2,3,4,5 and set the probability density function for the object within that shell to be p_i/v_i.What kind of an assumption do I need? Could you give an example?

The expected value is (0,0,0) if the probability distributions are spherically symmetric. Think about a probability distribution on a line. If it is symmetric about x = 0 then the mean value of the distribution must be x = 0.Also, if P = (0,0,0), how do you get the expected coordinates of the object to be (0,0,0)?

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