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Question: 2 letxgamma 2 4 ygam ma ...

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2. LetX-Gamma(α = 2, β = 4), Y-Gam ma (α = 3, β = 4), X & Y are independent, Z1 = , Z,-X + Y a) (3 pts) State the joint pdf ofX and Y. Simplify the expression, clearing all Гs. b) (9 pts) Find the joint pdf of Zi and Zz, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression(5 pts) You should see clearly that Zi and Z2 are independent. Therefore, without doing any integration clearly state the marginal pdfs of Zi and Z AND their supports. Furthermore, Zi and Z both are special distributions we have studied in this class; therefore, identify them by their names (read: Gamma, exponential, etc.) and their parameters. c)

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