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Problem 1. (5 marks. 3. 2) Assume X ~ Gamma(01, β) and Y ~ Gamma(O2, β) are independent random variables. a) Compute the Joint density of U = X + Y and V X X + Y , be sure to include the support/domain.
b) Based on the joint density derived in part (a) find the marginal densities of U and V, be sure to include the support (s)/domain(s). Explicitly state the name of the distributions of U and V and identify their parameters
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Transfoin) (X,y) → (U,V) )he re 美十 Lie. O,v 9%1-1 厂(4+41) tence U and V ae inde pendently dishibat

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