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Unformatted text preview: Y (c). the conditional p.d.f of X given Y = y (d). E ( Y  X ) and E ( X  Y ) (e). Cov ( X,Y ) (f). P ( Y ≤ X + 1) (g). Are X and Y independent ? 6 5. For each of the following questions, ±nd E ( X ) and V ar ( X ). (a). Suppose X  Y = y ∼ POI( y ), and Y ∼ GAM( α,β ) with the pdf f ( y ) = 1 Γ( α ) β α y α1 ey/β , for y > . (b). Suppose X  Y = y ∼ BIN( y,p ) and Y ∼ POI( λ ). (c). Suppose X  Y = y ∼ BIN( y + 1 ,p 1 ) and Y ∼ BIN( n,p 2 ). 7 6. Suppose X and Y have the joint pdf f ( x,y ) = exy , x > , y > , and zero otherwise. (a). Find P ( X + Y < 1). (b). Let U = X + Y , and V = X . Find the joint pdf of U and V ....
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 Spring '10
 Yi,GraceYun
 probability density function, joint PDF, Suppose

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