52. Let XI" '" X" be independent N( (J, y), 0 < y < 1 known, and Y1, · · · , Y" independent N((J,I). Then X is more informative than Y according to the definition at the end of Section 4.

[If V, is N(O, 1 - y), then X; + V, has the same distribution as .l Note. If a is unknown, it is not true that a sample from N(0, y( 2 ), 0< Y < 1, is more informative than one from N(O, ( 2 ); see Hansen ad Torgersen (1974).