Question: =+11. Suppose X has a continuous, strictly increasing distribution function F(x) and Y = X has distribution function G(y). Show that X is symmetrically distributed

=+11. Suppose X has a continuous, strictly increasing distribution function F(x) and Y = −X has distribution function G(y). Show that X is symmetrically distributed around some point μ if and only if the function x → x − G−1[F(x)] is constant, where G−1[G(y)] = y for all y.

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