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....
View
Full Document
 Fall '08
 Monrad
 Statistics, Probability, Probability distribution, Probability theory, probability density function, Cumulative distribution function, following random variables

Click to edit the document details