Unformatted text preview: Z = X + Y . Example 5: X and Y are jointly continuous with joint pdf f ( x,y ) = ± e( x + y ) if 0 ≤ x , 0 ≤ y , otherwise. Let Z = X/Y . Find the pdf of Z . Example 6: X and Y are independent, each with an exponential( λ ) distribution. Find the density of Z = X + Y and of W = YX 2 . Example 7: X and Y are jointly continuous with ( X,Y ) uniformly distributed over the union of the two squares { ( x,y ) : 0 ≤ x ≤ 1 , 1 ≤ y ≤ 1 } and { ( x,y ) : 0 ≤ x ≤ 1 , 3 ≤ y ≤ 4 } . (a). Find E ( Y ). (b). Find the marginal densities of X and Y . (c). Are X and Y independent? (d). Find the pdf of Z = X + Y ....
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 Spring '10
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 Probability distribution, probability density function, Cumulative distribution function, Joe Mitchell

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