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Unformatted text preview: (20) 2. Suppose X -U(0, 1) and Y * X = x -U(x, 1). Find the marginal p.d.f. of Y. (20) 3. Take a stick of unit length and break it at random. Let X be the break point. Then X -U(0, 1). Let Y be the length of the longer piece. What is the mean of Y? 4. Let the p.d.f. of the random variable Y be f Y (y) = &quot; y- ( &quot; + 1) for y $ 1, and equal to zero otherwise, where &quot; &gt; 0. (6) (a) Find the median of Y. (14) (b) Suppose you have a computer program to generate uniform random variables over [0, 1]. How can you use it to generate draws on the random variable Y? 5. Let X be a random variable with p.d.f. f(x) = c(1 + x)-2 for x &gt; 0, and zero otherwise, where c &gt; 0 is a constant. (5) (a) Find c. (5) (c) Let Y = &quot; + F R n(X). Find its p.d.f. . (5) (b) Find the c.d.f. of X. (5) (d) Find the c.d.f. of Y....
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This note was uploaded on 12/13/2011 for the course ECON 220a taught by Professor Poirier,d during the Fall '08 term at UC Irvine.
- Fall '08