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Unformatted text preview: Suppose that X and Y are independent, the p.d.f. of X is f X ( x ) = 2 / x 3 , x &gt; 1, zero otherwise, and Y has a Uniform distribution on interval ( 0, 1 ). Find the p.d.f. of W, f W ( w ) = f X + Y ( w ). Hint: Consider two cases: 1 &lt; w &lt; 2 and w &gt; 2. 2. (continued) Suppose that X and Y are independent, the p.d.f. of X is f X ( x ) = 2 / x 3 , x &gt; 1, zero otherwise, and Y has a Uniform distribution on interval ( 0, 1 ). b) Let V = X Y. Find the p.d.f. of V, f V ( v ) = f X Y ( v ). Hint: Consider two cases: 0 &lt; v &lt; 1 and v &gt; 1. c) Let U = Y / X . Find the c.d.f. and p.d.f. of U....
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This note was uploaded on 10/31/2011 for the course MATH 464 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Monrad
 Statistics, Probability

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