Let X, Y have the joint CDF for x > 0,y > 0 (and F(x, y) = 0 otherwise), where the parameter θ is a constant in [0, 1]. (a) Find the joint PDF of X, Y. For which values of θ (if any) are they...

for x > 0,y > 0 (and F(x, y) = 0 otherwise), where the parameter θ is a constant in [0, 1].

(a) Find the joint PDF of X, Y. For which values of θ (if any) are they independent?

(b) Explain why we require θ to be in [0, 1]

(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.