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Unformatted text preview: ) over the region R ( z ) , F Z ( z ) = Z Z R ( z ) f XY ( x , y ) dxdy . One Function of Two RVs: Method 1 Let Z = X + Y . Determine the cdf and pdf f Z ( z ) . (Cont.): The pdf of f Z ( z ) of Z = g ( X , Y ) is obtained by differentiating this cdf with respect to z . Note: Leibnitz rule: d dz Z b ( z ) a ( z ) g ( x , z ) dx = db ( z ) dz g ( b ( z ) , z )da ( z ) dz g ( a ( z ) , z )+ Z b ( z ) a ( z ) ∂ ∂ z g ( x , z ) dx One Function of Two RVs: Method 1 The random variables X and Y have joint density f X , Y ( x , y ) = ± ey ≤ x ≤ y < ∞ otherwise Find the probability density of the sum Z = X + Y . One Function of Two RVs: Method 1 Let Z = max ( X , Y ) . Determine the cdf and pdf f Z ( z ) . One Function of Two RVs: Method 1 The random variables X and Y have the joint density f X , Y ( x , y ) = ± x / y ≤ x ≤ y ≤ 2 otherwise Find the density of the product Z = XY ....
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 Fall '08
 DASILVER
 Probability theory, Cumulative distribution function, CDF, fz

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