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Unformatted text preview: X and diﬀerentiate to obtain a formula for the PDF of Y . 4. (From text) Let X and Y be the Cartesian coordinates of a randomly chosen point (according to a uniform PDF) in the triangle with vertices at (0,1), (0,1), and (1,0). Find the CDF and the PDF of Z =  XY  . 5. A particle’s velocity V is modeled as a normal random variable with mean 0 and variance σ 2 (we allow negative values). The particle’s energy is given by W = m V 2 2 , where m > 0 is a constant. (a) What is E [ W ] in terms of m and σ ? (b) What is the PDF of W ? 6. Extra Credit: Two points are chosen randomly and independently from the interval [0 , 1] according to a uniform distribution. Show that the expected distance between the two points is 1/3....
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This note was uploaded on 12/11/2011 for the course IEOR 3658 taught by Professor Olvera during the Fall '08 term at Columbia.
 Fall '08
 Olvera

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