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Unformatted text preview: F if for every x , lim n P ( n Y n x ) = F ( x ) . Find the cumulative distribution F to which n Y n converges weakly. What is the name of this distribution? 7. The joint density of X and Y is given by f ( x,y ) = e-y y , < x < y, < y < . Verify that this is a joint density. Find E [ X 2 | Y = y ]. 8. The joint density of X and Y is given by f ( x,y ) = e-x/y e-y y , < x < , < y < . Verify that this is a joint density. Find marginal density of Y . Show E [ X | Y = y ] = y . 9. Let X be exponential distribution with parameter . What is the distribution of ( X | X > 1)? Find E [ X | X > 1]. 10. Let X be uniform over (0 , 1). What is the distribution of ( X | X < 1 / 2)? Find E [ X | X < 1 / 2]. 2...
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This note was uploaded on 09/30/2010 for the course STATISTICS 36-217 taught by Professor Jin during the Fall '09 term at Carnegie Mellon.
- Fall '09