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Unformatted text preview: (b). Problem 3. The length X of a side of a cube has pdf f X ( x ) = x-2 , for 1 x . Find the pdf of the surface area of the cube. Problem 4. Suppose you can generate iid uniform (0,1) random variables U 1 ,U 2 ,... . Use them to generate n independent Gamma( m, ) random variables, where n and m are positive integers and > 0. Problem 5. A random vector ( X,Y ) has joint pdf f X,Y ( x,y ) = ( e-y if 0 < x < y, otherwise . Find the joint pdf of Z = Y-X and V = X . Are Z and V independent? The following problem is optional for students enrolled in 360, required for students enrolled in 560. Problem 6. A point in the plane is generated at random according to the following scheme. A radius R is generated from the 2 2 distribution. Independently, an angle is generated from the U (0 , 2 ) distribution. Find the joint distribution of X = R cos and Y = R sin ....
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This note was uploaded on 11/12/2008 for the course ORIE 360 taught by Professor Ehrlichman during the Fall '07 term at Cornell University (Engineering School).
- Fall '07