Show that Y X is a complete sufficient statistic for 0, where X has the pdf fX(x ) 1 (2), for x , zero elsewhere Show that Y X and Z sgn(X) are independent

Question: Show that Y = |X| is a complete sufficient statistic for > 0, where X has the pdf fX(x; ) = 1/(2), for

Show that Y = |X| is a complete sufficient statistic for θ > 0, where X has the pdf fX(x; θ) = 1/(2θ), for −θ < x < θ, zero elsewhere. Show that Y = |X| and Z = sgn(X) are independent.

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