Let X, Y have the joint CDF F(x, y)=1 e x e y + e (x+y+xy) , for x > 0,y > 0 (and F(x
Chapter 7, Problem 30(choose chapter or problem)
Let X, Y have the joint CDF F(x, y)=1 e x e y + e (x+y+xy) , for x > 0,y > 0 (and F(x, y) = 0 otherwise), where the parameter is a constant in [0, 1]. (a) Find the joint PDF of X, Y . For which values of (if any) are they independent? (b) Explain why we require to be in [ (c) Find the marginal PDFs of X and Y by working directly from the joint PDF from (a). When integrating, do not use integration by parts or computer assistance; rather, pattern match to facts we know about moments of famous distributions. (d) Find the marginal CDFs of X and Y by working directly from the joint CDF.
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