08SimHw2 - IEOR 4404 Assignment #2 Simulation September 17,...

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Unformatted text preview: IEOR 4404 Assignment #2 Simulation September 17, 2008 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #2 due September 23rd, 2008 1. Suppose that X and Y are jointly discrete random variables with p ( x,y ) = x + y 30 , for x = 0 , 1 , 2 and y = 0 , 1 , 2 , 3 , otherwise. (a) Compute and plot p X ( x ) and p Y ( y ). (b) Are X and Y independent? (c) Compute and plot F X ( x ) and F Y ( y ). (d) Compute E [ X ], var( X ), E [ Y ], var( Y ), cov( X,Y ) and corr( X,Y ). 2. A particles velocity V is normally distributed with mean 0 and variance 2 . The particles 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 ? (b) What is the PDF of W ? 3. If X and Y have a joint probability density function specified by f ( x,y ) = 2 e- ( x +2 y ) , < x < , < y < find P ( X < Y ). 4. For any random variables X 1 , X 2 and any numbers c 1 , c 2 , show that var( c 1 X 1 + c 2 X 2 ) = c 2 1 var( X 1 ) + 2 c 1 c 2 cov(...
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08SimHw2 - IEOR 4404 Assignment #2 Simulation September 17,...

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