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Unformatted text preview: & ² ³ ≥ < ≤< 5 1 5 2 21 4 2 2 x x x x Y = 2 X 1 . 2 < x < 5 ´ 25 1 < y < 4 1 . g ( x ) = 2 1 x g – 1 ( y ) = y 1 = y – 1 / 2 y x d d = – 2 1 y – 3 / 2 f Y ( y ) = f X ( g – 1 ( y ) ) y x d d = ( 21 2 y – 1 / 2 ) ( 2 1 y – 3 / 2 ) = 21 1 y – 2 , 25 1 < y < 4 1 . OR F Y ( y ) = P ( Y ≤ y ) = P ( 2 X 1 ≤ y ) = P ( X ≥ y 1 ) = 1 – P ( X < y 1 ) = 1 – F X ( y 1 ). = 1 – 21 4 1y = 21 25 1y , 25 1 < y < 4 1 . F Y ( y ) = & & & & ± & & & & ² ³ ≥ < ≤<4 1 1 4 1 25 1 21 25 25 1 1 y y y y f Y ( y ) = & & ± & & ² ³ < <otherwise 4 1 25 1 21 1 2 x y...
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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.
 Fall '08
 AlexeiStepanov
 Probability

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