HW11 ConvolutionPractice - Practice Problems: Computing the...

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Practice Problems: Computing the density of X + Y . 1) Let X Exp( λ ) and Y Exp( μ ), and let X and Y be independent. Compute the p.d.f. of X + Y . 1
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2) Let X and Y be independent with marginal density functions f X ( x ) = ± 2 x 0 x 1 0 otherwise and f Y ( y ) = ± 3 / 4(1 - y 2 ) - 1 y 1 0 otherwise . Compute the density of X + Y . 2
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3) Let X and Y be independent random variables such that X Exp(2) and Y U ( - 1 , 1). Compute the p.d.f. of X + Y . 3
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4) Let ( X, Y ) have joint p.d.f. f ( x, y ) = ± x + y 0 x, y 1 0 otherwise . a) Are X and Y independent? b) Compute the p.d.f. of Z = X + Y . 4
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5) Let X and Y be independent random variables with
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This note was uploaded on 09/05/2011 for the course MATH 4710 at Cornell University (Engineering School).

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HW11 ConvolutionPractice - Practice Problems: Computing the...

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