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Unformatted text preview: X . 2 3. [20 pts.] Calculate the PDF corresponding to the DF F ( x ) = , x x 2 / 2 , x 1 1(2x ) 2 / 2 , 1 x 2 1 , 2 x 3 4. [20 pts.] Suppose the random vector ( X,Y ) has the PDF f ( x,y ) = 4(1 + xy ) / 5 , < x < 1 , < y < 1 . Find the conditional expectation of Y given X . 4 5. [20 pts.] Suppose the conditional distribution of Y given X is NegBin( r,X ) where r is a known positive integer, and suppose the marginal distribution of X is Beta( 1 , 2 ). What is the conditional distribution of X given Y ? Since this is a brand name distribution, no integrals need be done, it is enough to name the distribution and give its parameters as a function of Y , r , 1 , and 2 . 5...
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 Fall '02
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