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I am reading an article and trying to extend their case to a multivariate case. I have the function

$f_{i} (x)=\frac{1}{|Σ|}f_{0}((x-μ_{i})'Σ^{-1}(x-μ_{i}))$, where $f_{0}(.)$ is a base density function.

I am trying to find $∫xf_i^2 (x)dx$

But the article does not provide any instructions or details about how they found their results.

Is there a good source that provide how a way of finding this expected value?

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  • $\begingroup$ Since you say nothing about $f_0,$ there's little one can say. Could you tell us what $f_0$ is? $\endgroup$
    – whuber ♦
    Oct 14, 2019 at 13:51
  • $\begingroup$ The article does not mention anything about $f_{0} (.)$ but the fact that it is a base density function. $\endgroup$
    – H A
    Oct 15, 2019 at 2:50
  • $\begingroup$ Then in what sense do you mean to "find" this integral? $\endgroup$
    – whuber ♦
    Oct 15, 2019 at 12:58
  • $\begingroup$ Can I write it in terms of integral or simplify it? and solve it for $\mu$? $\endgroup$
    – H A
    Oct 16, 2019 at 1:19
  • $\begingroup$ When $f_i$ is unspecified, there's no simplification. $\endgroup$
    – whuber ♦
    Oct 16, 2019 at 12:38

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