09_08 - STAT 410 Examples for Fall 2008 Example 9 2x 0 0 <...

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STAT 410 Examples for 09/08/2008 Fall 2008 Example 9 : f X ( x ) = ± ² < < o.w. 0 1 0 2 x x F X ( x ) = ³ ³ ± ² < < 1 1 1 0 0 0 2 x x x x Y = X . y < 0 F Y ( y ) = P ( Y y ) = P ( X y ) = 0. y 0 F Y ( y ) = P ( Y y ) = P ( X y ) = P ( X y 2 ) = F X ( y 2 ). 0 y < 1 F Y ( y ) = F X ( y 2 ) = y 4 . y 1 F Y ( y ) = F X ( y 2 ) = 1. F Y ( y ) = ³ ³ ± ² < < 1 1 1 0 0 0 4 y y y y f Y ( y ) = ³ ³ ± ² < < o.w. 0 1 0 4 3 y y - - - - - - - - - - - - - - Theorem 1.7.1 X – continuous r.v. with p.d.f. f X ( x ). Y = g ( X ) g ( x ) – one-to-one, differentiable d x / d y = d [ g 1 ( y ) ] / d y ´ f Y ( y ) = f X ( g 1 ( y ) ) y x d d
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This note was uploaded on 10/22/2009 for the course STAT 410 taught by Professor Alexeistepanov during the Fall '08 term at University of Illinois at Urbana–Champaign.

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09_08 - STAT 410 Examples for Fall 2008 Example 9 2x 0 0 <...

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