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Let x denote a p-variate random vector. Let F x denote the cumulative distribution function of x. Assume that x is symmetrically distributed about .

Let x denote a p-variate random vector. Let Fx denote the cumulative distribution function of x.

Assume that x is symmetrically distributed about . Assume that T is an affine equivariant location functional

and assume that T(Fx) exists as a finite quantity.

Show that T(Fx)= .

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