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Unformatted text preview: ey/β , y > , respectively. (1). Find P ( X > Y ). (2). Find P ( X > 2 Y ). 5 4. For each of the following questions, ﬁnd 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 ). 6 5. Let X and Y have the joint density f ( x,y ) = ey , ≤ x ≤ y (a) Find COV ( X,Y ) and correlation of X and Y (b) Find E ( X  Y = y ) and E ( Y  X = x ) (c) Find the density functions of the random variables E ( X  Y ) and E ( Y  X ) 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 '08
 PAULASMITH
 Statistics, Normal Distribution, Probability theory, probability density function, Cumulative distribution function, joint PDF, marginal pdf

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